7 Tenths As A Fraction

In this affiliate you volition learn how to say precisely how long something is. With whole numbers only, nosotros cannot always say precisely how long something is. Fractions were invented for that purpose. You will also learn to calculate with fractions.

Measuring accurately with parts of a unit of measurement

A strange measuring unit

In this activeness, you will measure lengths with a unit called a greystick. The grey measuring stick below is exactly one greystick long. Yous will utilise this stick to mensurate dissimilar objects.

The red bar beneath is exactly 2 greysticks long.

Equally you tin can encounter, the xanthous bar beneath is longer than 1 greystick but shorter than 2 greysticks.

To endeavour to measure the yellow bar accurately, we will dissever one greystick into six equal parts:

So each of these parts is ane 6th of a greystick.

Do you think one can say the yellow bar is one and four sixths of a greystick long?
Draw the length of the blue bar in words.

This greystick ruler is divided into seven equal parts:

Each part is ane seventh of a greystick.
In each case beneath, say what the smaller parts of the greystick may be called. Write your answers in words.
How did yous observe out what to call the pocket-sized parts?

Write all your answers to the following questions in words.
1. How long is the upper xanthous bar?
2. How long is the lower xanthous bar?
1. How long is the blue bar at the bottom of the previous folio?
2. How long is the reddish bar at the bottom of the previous page?
1. How many twelfths of a greystick is the same length as ane sixth of a greystick?
2. How many twenty-fourths is the same length every bit i sixth of a greystick?
3. How many twenty-fourths is the same length as 7 twelfths of a greystick?
1. How long is the upper yellow bar below?
2. How long is the lower yellow bar above?
3. How long is the bluish bar?
4. How long is the crimson bar?
1. How many fifths of a greystick is the aforementioned length as 12 twentieths of a greystick?
2. How many fourths (or quarters) of a greystick is the aforementioned length equally 15 twentieths of a greystick?

Draw the aforementioned length in dissimilar ways

Ii fractions may draw the same length. You can run into here that 3 sixths of a greystick is the same every bit 4 eighths of a greystick.

When two fractions describe the aforementioned portion we say they are equivalent.

1. What can each pocket-size part on this greystick be called?
2. How many eighteenths is 1 sixth of the greystick?
3. How many eighteenths is one third of the greystick?
4. How many eighteenths is five sixths of the greystick?
1. Write (in words) the names of four different fractions that are all equivalent to three quarters. You lot may await at the yellow greysticks on page 154 to aid y'all.
2. Which equivalents for 2 thirds can you find on the yellow greysticks?

The information that ii thirds is equivalent to 4 sixths, to 6 ninths and to eight twelfths is written in the second row of the table below. Complete the other rows of the table in the same way. The diagrams on page 154 may aid yous.

thirds	fourths	fifths	sixths	eighths	ninths	tenths	twelfths	twentieths
i
2	-	-	4	-	vi	-	8	-
-	iii
-	-	ane
-	-	two
-	-	three
-	-	four

Complete this table in the same way every bit the table in question 3.

fifths	tenths	fifteenths	twentieths	twenty-fifths	fiftieths	hundredths
1
2
three
4
5
6
7

Draw on the greysticks beneath to show that 3 fifths and 9 fifteenths are equivalent. Describe freehand; you need not mensurate and describe accurately.

Consummate these tables in the aforementioned manner as the table in question 4.

eighths	sixteenths	24ths
1
ii
iii
4
v
6
7
8
ix

24ths	sixths	twelfths	18ths
	one
	2
	3
	4
	five
	6
	seven
	8
	nine

1. How much is 5 twelfths plus three twelfths?
2. How much is five twelfths plus one quarter?
3. How much is five twelfths plus three quarters?
4. How much is one third plus one quarter? It may help if yous piece of work with the equivalent fractions in twelfths.

Unlike parts in different colours

This strip is divided into 8 equal parts.

Five eighths of this strip is ruddy.

What part of the strip is bluish?
What part of this strip is yellow?
What part of the strip is blood-red?
What part of this strip is coloured blue and what role is coloured scarlet?
1. What part of this strip is blue, what part is red and what part is white?
2. Limited your respond differently with equivalent fractions.
A certain strip is not shown here. 2 ninths of the strip is blue, and iii ninths of the strip is green. The balance of the strip is red. What part of the strip is red?
What office of the strip below is yellow, what role is bluish, and what role is red?

The number of parts in a fraction is called the numerator of the fraction. For example, the numerator in 5 sixths is five.

The blazon of part in a fraction is called the denominator. Information technology is the name of the parts that are beingness referred to and it is adamant by the size of the function. For case, sixths is the denominator in v sixths.

To enumerate means "to detect the number of".

To denominate means "to give a name to".

\( ^5/_6 \) is a short way to write v sixths.

Nosotros may also write \(\frac{five}{6}\)

Fifty-fifty when we write \( ^5/_6 \) or \(\frac{five}{6}\), we however say "5 sixths".

\( ^\text{ }/_6 \) and \(\frac{\text{ }}{half dozen}\) are short ways to write sixths.

The numerator (number of parts) is written higher up the line of the fraction: \(\frac{\textit{numerator}}{\text{...}}\)

The denominator is indicated by a number written beneath the line: \(\frac{\text{...}}{\textit{denominator}}\)

Consider the fraction 3 quarters. It can be written as \(\frac{iii}{4}\).
1. Multiply both the numerator and the denominator by two to form a new fraction. Is the new fraction equivalent to \(\frac{three}{4}\)? You may check on the diagram below.
2. Multiply both the numerator and the denominator by 3 to form a new fraction. Is the new fraction equivalent to \(\frac{3}{four}\)?
3. Multiply both the numerator and the denominator past 4 to class a new fraction. Is the new fraction equivalent to \(\frac{three}{4}\)?
4. Multiply both the numerator and the denominator by 6 to form a new fraction. Is the new fraction equivalent to \(\frac{3}{4}\)?

Combining fractions

Bigger and smaller parts

Gertie was asked to solve this problem:

A team of road-builders built \(\frac{8}{12}\) km of route in one week, and \(\frac{10}{12}\) km in the next week. What is the full length of road that they built in the ii weeks?

She idea like this to solve the problem:

\(\frac{8}{12}\) is 8 twelfths and\(\frac{10}{12}\) is 10 twelfths, so birthday it is eighteen twelfths.

I can write\(\frac{18}{12}\) or "eighteen twelfths".

I can besides say 12 twelfths of a km is 1 km, then xviii twelfths is i km and half dozen twelfths of a km.

This I can write every bit \(i\frac{6}{12}\). It is the same as \(1\frac{one}{2}\)km.

Gertie was likewise asked the question: How much is \(4\frac{5}{9} + 2\frac{7}{9}\) ?

She thought like this to answer it:

\(4\frac{five}{9}\) is iv wholes and 5 ninths, and \(2\frac{7}{9}\) is 2 wholes and vii ninths.

And then birthday it is 6 wholes and 12 ninths. Just 12 ninths is 9 ninths (1 whole) and three ninths, so I can say it is seven wholes and 3 ninths.

I can write \(7\frac{three}{9}\).

Would Gertie be wrong if she said her answer was \(vii\frac{1}{three}\)?
Senthereng has \(4\frac{seven}{12}\) bottles of cooking oil. He gives \(one\frac{five}{12}\) bottles to his friend Willem. How much oil does Senthereng have left?
Margaret has \(v\frac{5 }{8 }\) bottles of cooking oil. She gives \(3\frac{7 }{ 8}\) bottles to her friend Naledi. How much oil does Margaret have left?
Summate each of the following:
1. \(4\frac{ii}{7} - iii\frac{6}{7}\)
2. \(3\frac{6}{7} + \frac{3}{7}\)
3. \(iii\frac{six}{7} + ane\frac{4}{5}\)
4. \(4\frac{iii}{8} - 2\frac{iv}{5}\)
5. \(1\frac{3}{10} - \frac{two}{three}\)
6. \(iii\frac{5}{10} - 1\frac{1}{two}\)
7. \(\frac{5}{eight} + \frac{five}{8} + \frac{5}{8} + \frac{v}{8} + \frac{v}{8}\)
8. \(six\frac{2}{five} + two\frac{one}{4} -\frac{one}{ii}\)
9. \(\frac{v}{8} + \frac{5}{8} + \frac{v}{8} + \frac{5}{8} + \frac{v}{8} + \frac{5}{8} + \frac{five}{8} + \frac{5}{8} + \frac{5}{8} + \frac{five}{eight} + \frac{five}{viii} + \frac{5}{viii} + \frac{5}{8}\)
10. \(two\frac{4}{seven} + 2\frac{4}{vii} + ii\frac{4}{7} + two\frac{4}{vii} + 2\frac{four}{vii} + 2\frac{4}{7} + 2\frac{4}{7} + two\frac{iv}{7}\)
11. \((4\frac{2}{7} + ane\frac{4}{seven}) - 2\frac{i}{iii}\)
12. \((2\frac{7}{10} + 3\frac{3}{5}) - (1\frac{ii}{5} + iii\frac{7}{10})\)
Neo'southward report had five chapters. The first affiliate was \(\frac{3 }{4 }\) of a page, the 2d chapter was \(two\frac{1 }{ii }\) pages, the third chapter was \(3\frac{3 }{iv }\) pages, the fourth chapter was iii pages and the fifth chapter was \(1\frac{1 }{ii }\) pages. How many pages was Neo's report in total?

Tenths and hundredths (percentages)

1. 100 children each get 3 biscuits. How many biscuits is this in full?
2. 500 sweets are shared every bit between 100 children. How many sweets does each kid go?
The picture beneath shows a strip of licorice. The very small pieces can hands be broken off on the thin lines. How many very small pieces are shown on the picture?
Gatsha runs a spaza shop. He sells strips of licorice similar the above for R2 each.
1. What is the price of one very small-scale piece of licorice, when you buy from Gatsha?
2. Jonathan wants to buy one fifth of a strip of licorice. How much should he pay?
3. Batseba eats 25 very small pieces. What part of a whole strip of licorice is this?
Each small-scale piece of the to a higher place strip is one hundredth of the whole strip.
1. Why tin can each modest piece be called one hundredth of the whole strip?
2. How many hundredths is the aforementioned as one tenth of the strip?
Gatsha often sells parts of licorice strips to customers. He uses a "quarters marker" and a "fifths mark" to cut off the pieces correctly from full strips. His two markers are shown below, next to a total strip of licorice.
1. How many hundredths is the aforementioned equally two fifths of the whole strip?
2. How many tenths is the aforementioned equally \(\frac{two }{5 }\) of the whole strip?
3. How many hundredths is the same as \(\frac{three }{iv }\) of the whole strip?
4. Freddie bought \(\frac{lx }{100 }\) of a strip. How many fifths of a strip is this?
5. Jamey bought part of a strip for R1,60. What part of a strip did she buy?
Gatsha, the owner of the spaza shop, sold pieces of yellow licorice to different children. Their pieces are shown beneath. How much (what part of a whole strip) did each of them go?
The yellow licorice shown above costs R2,40 (240 cents) for a strip. How much does each of the children have to pay? Circular off the amounts to the nearest cent.
1. How much is \(\frac{1 }{100 }\) of 300 cents?
2. How much is \(\frac{7 }{100 }\) of 300 cents?
3. How much is \(\frac{25}{100}\) of 300 cents?
4. How much is \(\frac{ane}{four}\) of 300 cents?
5. How much is \(\frac{twoscore}{100}\) of 300 cents?
6. How much is \(\frac{2}{five}\) of 300 cents?
Explicate why your answers for questions eight(e) and 8(f) are the same.

Another discussion for hundredth is per cent.

Instead of saying

Miriam received 32 hundredths of a licorice strip, we can say

Miriam received 32 per cent of a licorice strip.

The symbol for per cent is %.
How much is 80% of each of the following?
1. R500
2. R480
3. R850
4. R2400
How much is 8% of each of the amounts in 10(a), (b), (c) and (d)?
How much is 15% of each of the amounts in 10(a), (b), (c) and (d)?
Building costs of houses increased by 20%. What is the new building cost for a business firm that previously cost R110 000 to build?
The value of a car decreases by 30% after ane year. If the price of a new car is R125 000, what is the value of the car afterward ane year?
Investigate which denominators of fractions tin easily be converted to powers of x.

Thousandths, hundredths and tenths

Many equal parts

In a camp for refugees, fifty kg of saccharide must be shared equally between 1 000 refugees. How much sugar will each refugee become? Go on in mind that 1 kg is 1 000 g. You lot can give your answer in grams.
How much is each of the following?
1. i tenth of R6 000
2. one hundredth of R6 000
3. i thousandth of R6 000
4. x hundredths of R6 000
5. 100 thousandths of R6 000
6. seven hundredths of R6 000
7. 70 thousandths of R6 000
8. seven thousandths of R6 000
Calculate.
1. \(\frac{3}{10} +\frac{five}{8}\)
2. \(iii\frac{3}{10} + 2\frac{4}{5}\)
3. \(\frac{three}{10} + \frac{7}{100}\)
4. \(\frac{iii}{10} + \frac{70}{100}\)
5. \(\frac{3}{x} + \frac{7}{1000}\)
6. \(\frac{three}{10} + \frac{70}{1000}\)
Calculate.
1. \(\frac{3}{ten} + \frac{seven}{100} +\frac{4}{thousand}\)
2. \(\frac{3}{10} + \frac{70}{100} +\frac{400}{1000}\)
3. \(\frac{half-dozen}{x} + \frac{20}{100} +\frac{700}{m}\)
4. \(\frac{2}{10} + \frac{5}{100} +\frac{four}{1000}\)
In each case investigate whether the argument is true or not, and give reasons for your terminal decision.
1. \(\frac{1}{10} + \frac{23}{100} + \frac{346}{grand} = \frac{6}{10} + \frac{3}{100} + \frac{46}{chiliad}\)
2. \(\frac{1}{ten} + \frac{23}{100} + \frac{346}{1000} = \frac{7}{ten} + \frac{2}{100} + \frac{vi}{1000}\)
3. \(\frac{ane}{10} + \frac{23}{100} + \frac{346}{1000} = \frac{6}{10} + \frac{7}{100} + \frac{46}{1000}\)
4. \(\frac{676}{1000} = \frac{6}{10} + \frac{7}{100} + \frac{6}{g}\)

Fraction of a fraction

Form parts of parts

1. How much is 1 fifth of R60?
2. How much is iii fifths of R60?
How much is seven tenths of R80? (You may first work out how much one tenth of R80 is.)
In the The states the unit of currency is the US dollar, in United kingdom it is the pound, in Western Europe the euro, and in Botswana the pula.
1. How much is ii fifths of 20 pula?
2. How much is ii fifths of 20 euro?
3. How much is 2 fifths of 12 pula?
Why was it so easy to calculate 2 fifths of 20, just difficult to summate two fifths of 12?

In that location is a way to go far easy to calculate something similar iii fifths of R4. Y'all just change the rands to cents!
Summate each of the post-obit. You lot may change the rands to cents to brand it easier.
1. three eighths of R2,twoscore
2. 7 twelfths of R6
3. 2 fifths of R21
4. 5 sixths of R3
You will now practise some calculations about hole-and-corner objects.
1. How much is 3 tenths of forty secret objects?
2. How much is three eighths of 40 undercover objects?
The cloak-and-dagger objects in question 6 are fiftieths of a rand.
1. How many fiftieths is 3 tenths of forty fiftieths?
2. How many fiftieths is 5 eighths of 40 fiftieths?
1. How many twentieths of a kilogram is the same as \(\frac{3 }{4 }\) of a kilogram?
2. How much is one 5th of 15 rands?
3. How much is ane fifth of 15 twentieths of a kilogram?
4. So, how much is 1 5th of \(\frac{three }{4 }\) of a kilogram?
1. How much is \(\frac{ane}{12}\) of 24 fortieths of some secret object?
2. How much is \(\frac{7 }{12}\) of 24 fortieths of the secret object?
Do you lot agree that the answers for the previous question are 2 fortieths and 14 fortieths? If yous disagree, explain why you disagree.
1. How much is \(\frac{1 }{5 }\) of 80?
2. How much is \(\frac{3 }{5 }\) of eighty?
3. How much is \(\frac{1 }{40 }\) of 80?
4. How much is \(\frac{24 }{40 }\) of lxxx?
5. Explain why \(\frac{3 }{five }\) of eighty is the same as \(\frac{24 }{40 }\) of 80.
Look again at your answers for questions nine(b) and 11(e). How much is \(\frac{7 }{12 }\) of \(\frac{3 }{v}\)? Explain your respond.

The hugger-mugger object in question 9 was an envelope with R160 in information technology.

After the work you did in questions 9, x and 11, you know that

\(\frac{24 }{40 }\) and \(\frac{3 }{5 }\) are just two means to describe the aforementioned affair, and
\(\frac{7 }{12 }\) of \(\frac{3 }{5 }\) is therefore the same as \(\frac{7 }{12 }\) of \(\frac{24 }{twoscore }\) .

Information technology is easy to summate \(\frac{seven }{12 }\) of \(\frac{24 }{40 }\) : one twelfth of 24 is 2, so 7 twelfths of 24 is 14, so

7 twelfths of 24 fortieths is xiv fortieths.

\(\frac{3 }{8 }\) of \(\frac{2 }{three }\) tin can be calculated in the same way. But ane eighth of \(\frac{two }{iii }\) is a slight problem, and so information technology would be improve to use some equivalent of \(\frac{2 }{3 }\). The equivalent should be chosen and so that it is easy to summate ane eighth of it; then it would be dainty if the numerator could be 8.

\(\frac{8 }{12 }\) is equivalent to \(\frac{ii }{3 }\), and so instead of calculating \(\frac{3 }{eight }\) of \(\frac{2 }{three }\) nosotros may calculate \(\frac{three }{eight }\) of \(\frac{8 }{12 }\).

1. Calculate \(\frac{3 }{8 }\) of \(\frac{8 }{12 }\).
2. So, how much is \(\frac{3 }{8 }\) of \(\frac{2 }{3 }\)?
In each case replace the second fraction by a suitable equivalent, and so summate.
1. How much is \(\frac{iii }{four }\) of \(\frac{five }{8 }\)?
2. How much is \(\frac{seven }{10}\) of \(\frac{2 }{three }\)?
3. How much is \(\frac{2 }{3 }\) of \(\frac{1 }{2 }\)?
4. How much is \(\frac{iii }{v }\) of \(\frac{three }{v }\)?

Multiplying with fractions

Parts of rectangles, and parts of parts

1. Carve up the rectangle on the left into eighths by cartoon vertical lines. Lightly shade the left 3 eighths of the rectangle.
2. Split the rectangle on the correct into fifths drawing horizontal lines. Lightly shade the upper 2 fifths of the rectangle.
1. Shade 4 sevenths of the rectangle on the left below.
2. Shade 16 twenty-eighths of the rectangle on the right beneath.
1. What function of each big rectangle below is coloured yellow?
2. What part of the yellow part of the rectangle on the right is dotted?
3. Into how many squares is the whole rectangle on the correct divided?
4. What role of the whole rectangle on the right is yellow and dotted?
Make diagrams on the grid beneath to help yous to figure out how much each of the post-obit is:
1. \(\frac{3}{4}\) of \(\frac{5}{8}\)
2. \(\frac{2}{3}\) of \(\frac{4}{5}\)
Here is something you can do with the fractions \(\frac{3}{4}\) and \(\frac{five}{viii}\) :

Multiply the ii numerators and make this the numerator of a new fraction. Also multiply the 2 denominators, and make this the denominator of a new fraction \(\frac{3 \times 5}{4 \times 8} = \frac{15}{32}\).
Compare the above with what you did in question 14(a) of department 6.6 and in question iv(a) at the top of this folio. What do yous notice about \(\frac{3}{4}\) of \(\frac{5}{8}\) and \(\frac{3 \times 5}{4 \times 8} = \frac{15}{32}\)?
1. Alan has 5 heaps of 8 apples each. How many apples is that in total?
2. Sean has 10 heaps of 6 quarter apples each. How many apples is that in total?
Instead of saying \(\frac{5}{8}\) of R40 or \(\frac{5}{8}\) of \(\frac{2}{3}\) of a floor surface, we may say \(\frac{5}{8} \times \) R40 or \(\frac{5}{8} \times \frac{2}{3}\) of a floor surface.
Apply the diagrams below to figure out how much each of the following is:
1. \(\frac{iii}{10} \times \frac{v}{6}\)
2. \(\frac{ii}{5} \times \frac{7}{8}\)
1. Perform the calculations \(\frac{\text{numerator} \times \text{numerator}}{\text{denominator} \times \text{denominator}}\) for \(\frac{iii}{10}\) and \(\frac{v}{6}\) and compare the answer to your answer for question vii(a).
2. Do the aforementioned for \(\frac{2}{v}\) and \(\frac{vii}{8}\)
Perform the calculations \(\frac{\text{numerator} \times \text{numerator}}{\text{denominator} \times \text{denominator}}\) for
1. \(\frac{five}{6}\) and \(\frac{seven}{12}\)
2. \(\frac{iii}{4}\) and \(\frac{two}{iii}\)
Use the diagrams beneath to cheque whether the formula \(\frac{\text{numerator} \times \text{numerator}}{\text{denominator} \times \text{denominator}}\) produces the correct answers for \(\frac{5}{6} \times \frac{7}{12}\) and \(\frac{3}{4} \times \frac{2}{3}\).
Calculate each of the post-obit:
1. \(\frac{1}{2}\) of \(\frac{one}{3}\) of R60
2. \(\frac{2}{7}\) of \(\frac{two}{9}\) of R63
3. \(\frac{4}{3}\) of \(\frac{two}{v}\) of R45
1. John normally practises soccer for three quarters of an hour every day. Today he practised for only half his usual time. How long did he practise today?
2. A bag of peanuts weighs \(\frac{3}{8}\) of a kilogram. What does \(\frac{three}{4}\) of a handbag weigh?
3. Summate the mass of \(7\frac{three}{8}\) packets of sugar if i packet has a mass of \(\frac{3}{iv}\) kg.

Ordering and comparing fractions

Guild the following from the smallest to the biggest:
1. \( \frac{7}{16}\); \( \frac{3}{8}\); \( \frac{11}{24}\) ;\( \frac{5}{12}\); \( \frac{23}{48}\);
2. \( \frac{703}{1000}\); \( \frac{13}{20}\); \( \frac{vii}{10}\); 73%; \( \frac{71}{100}\);
Order the post-obit from biggest to the smallest:
1. \( \frac{41}{60}\); \( \frac{nineteen}{thirty}\); \( \frac{vii}{10}\) ;\( \frac{11}{15}\); \( \frac{17}{20}\);
2. \( \frac{23}{24}\); \( \frac{2}{iii}\); \( \frac{seven}{8}\); \(\frac{19}{20}\); \( \frac{5}{6}\);
Employ the symbols \(=\), \(\gt\) or \(\lt\) to make the following true:
1. \(\frac{7}{17}\) ☐ \(\frac{21}{51}\)
2. \(\frac{1}{17}\) ☐ \(\frac{1}{19}\)

Do the calculations given below. Rewrite each question in the mutual fraction notation. So write the reply in words and in the mutual fraction annotation.
1. 3 twentieths + v twentieths
2. 5 twelfths + xi twelfths
3. 3 halves + five quarters
4. 3 fifths + three tenths
Complete the equivalent fractions.
1. \(\frac{5}{7} = \frac{☐}{49}\)
2. \(\frac{ix}{11} = \frac{☐}{33}\)
3. \(\frac{15}{ten} = \frac{3}{☐}\)
4. \(\frac{i}{9} = \frac{four}{☐}\)
5. \(\frac{45}{eighteen} = \frac{☐}{2}\)
6. \(\frac{four}{5} = \frac{☐}{35}\)
Practise the calculations given below. Rewrite each question in words. Then write the respond in words and in the mutual fraction notation.
1. \(\frac{3}{10} + \frac{seven}{30}\)
2. \(\frac{2}{v} + \frac{vii}{12}\)
3. \(\frac{1}{100} + \frac{7}{ten}\)
4. \(\frac{iii}{5} - \frac{iii}{eight}\)
5. \(2\frac{iii}{10} + 5\frac{9}{10}\)
Joe earns R5 000 per month. His bacon increases past 12%. What is his new salary?
Ahmed earned R7 500 per calendar month. At the end of a sure month, his employer raised his salary by 10%. Yet, one month later his employer had to subtract his salary again by 10%. What was Ahmed'due south salary and so?
Calculate each of the following and simplify the answer to its lowest form:
1. \(\frac{thirteen}{20} - \frac{two}{5}\)
2. \(3\frac{24}{100} - 1\frac{two}{10}\)
3. \(v\frac{ix}{xi} - 2\frac{ane}{iv}\)
4. \(\frac{2}{iii} + \frac{4}{vii}\)
Evaluate.
1. \(\frac{1}{ii} \times 9\)
2. \(\frac{3}{v} \times \frac{10}{27}\)
3. \(\frac{ii}{3} \times xv\)
4. \(\frac{2}{3} \times \frac{3}{4}\)
Summate.
1. \(2\frac{2}{3} \times ii\frac{2}{3}\)
2. \(8\frac{ii}{5} \times 3\frac{one}{3}\)
3. \((\frac{one}{3} +\frac{1}{2}) \times \frac{6}{vii}\)
4. \(\frac{2}{3} \times \frac{one}{ii} \times \frac{3}{4}\)
5. \(\frac{5}{six} + \frac{2}{3} \times \frac{1}{5}\)
6. \(\frac{3}{four} - \frac{two}{five} \times \frac{5}{6}\)