In this thing you will certainly learn exactly how to say exactly how lengthy something is. With whole numbers only, we cannot constantly say precisely how long something is. Fractions were created for that purpose. You will additionally learn come calculate through fractions.

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Measuring that s right with parts of a unit

A strange measuring unit

In this activity, you will measure lengths through a unit called a greystick. The grey measure up stick listed below is exactly 1 greystick long. You will usage this stick come measure different objects.

The red bar listed below is precisely 2 greysticks long.

As you can see, the yellow bar below is longer than 1 greystick but shorter than 2 greysticks.

To shot to measure up the yellow bar accurately, we will divide one greystick into six equal parts:

So every of these components is one sixth of a greystick.

do you think one deserve to say the yellow bar is one and also four sixths the a greystick long?

Describe the size of the blue bar in words.

This greystick ruler is divided into 7 equal parts:

Each component is one seventh that a greystick.

In each situation below, say what the smaller parts of the greystick may be called. Write your answers in words.

How did you uncover out what to speak to the little parts?

How lengthy is the top yellow bar?

How long is the lower yellow bar?

How long is the blue bar at the bottom the the ahead page?

How long is the red bar at the bottom of the vault page?

How plenty of twelfths of a greystick is the same size as one sixth of a greystick?

How numerous twenty-fourths is the same length as one 6th of a greystick?

How countless twenty-fourths is the same size as seven twelfths of a greystick?

How long is the upper yellow bar below?

How lengthy is the reduced yellow bar above?

How lengthy is the blue bar?

How lengthy is the red bar?

How numerous fifths that a greystick is the same length as 12 twentieths of a greystick?

How numerous fourths (or quarters) that a greystick is the same size as 15 twentieths of a greystick?

Describe the same size in different ways

Two fractions may explain the exact same length. You deserve to see below that 3 sixths that a greystick is the very same as four eighths of a greystick.

When two fractions explain the same section we speak they room equivalent.

What deserve to each small part on this greystick it is in called?

How numerous eighteenths is one 6th of the greystick?

How plenty of eighteenths is one 3rd of the greystick?

How numerous eighteenths is five sixths the the greystick?

write (in words) the surname of four different fractions that space all identical to three quarters. You might look in ~ the yellow greysticks on web page 154 to help you.

Which equivalents for two thirds deserve to you find on the yellow greysticks?

The info that 2 thirds is identical to 4 sixths, to 6 ninths and also to 8 twelfths is created in the 2nd row of the table below. Finish the other rows of the table in the very same way. The diagrams on page 154 may help you.

2

-

-

-

-

 thirds fourths fifths sixths eighths ninths tenths twelfths twentieths 1 - - 4 - 6 - 8 - - 3 - 1 - 2 - 3 - 4

finish this table in the same means as the table in question 3.

fifths

2

3

4

5

6

7

 tenths fifteenths twentieths twenty-fifths fiftieths hundredths 1

attract on the greysticks below to display that 3 fifths and 9 fifteenths room equivalent. Attract freehand; you need not measure and also draw accurately.

Complete these tables in the same means as the table in question 4.

eighths

2

3

4

5

6

7

8

9

 sixteenths 24ths 1

24ths

2

3

4

5

6

7

8

9

 sixths twelfths 18ths 1

exactly how much is five twelfths plus 3 twelfths?

how much is five twelfths add to one quarter?

How lot is 5 twelfths plus three quarters?

How much is one third plus one quarter? that may assist if you work-related with the equivalent fractions in twelfths.

Different components in various colours

This piece is separated into eight equal parts.

Five eighths that this piece is red.

What part of the strip is red?

What part of this strip is coloured blue and what component is coloured red?

What component of this piece is blue, what part is red and also what component is white?

Express her answer in different way with indistinguishable fractions.

A specific strip is not displayed here. Two ninths of the piece is blue, and also three ninths of the piece is green. The rest of the strip is red. What part of the piece is red?

What component of the strip listed below is yellow, what component is blue, and also what part is red?

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

The type of part in a portion is dubbed the denominator. That is the name of the components that space being advert to and it is identified by the dimension of the part. For example, sixths is the denominator in 5 sixths.

( ^5/_6 ) is a short method to create 5 sixths.

Even once we compose ( ^5/_6 ) or (frac56), we still say "5 sixths".

( ^ ext /_6 ) and (frac ext 6) are brief ways to write sixths.

The numerator (number of parts) is written over the heat of the fraction: (frac extitnumerator ext...)

The denominator is suggested by a number written below the line: (frac ext... extitdenominator)

take into consideration the fraction 3 quarters. It have the right to be created as (frac34).

Multiply both the numerator and also the denominator by 2 to form a brand-new fraction. Is the new portion equivalent to (frac34)? friend may inspect on the diagram below.

main point both the numerator and the denominator through 3 to type a new fraction. Is the new portion equivalent to (frac34)?

Multiply both the numerator and also the denominator by 4 to type a brand-new fraction. Is the new portion equivalent come (frac34)?

Multiply both the numerator and the denominator by 6 to type a brand-new fraction. Is the new fraction equivalent come (frac34)?

Combining fractions

Bigger and smaller parts

Gertie to be asked to solve this problem:

A team of road-builders built (frac812) kilometres of roadway in one week, and also (frac1012) kilometres in the following week. What is the total length of roadway that they developed in the 2 weeks?

She thought choose this to resolve the problem:

(frac812) is eight twelfths and(frac1012) is ten twelfths, so completely it is eighteen twelfths.

I deserve to write(frac1812) or "18 twelfths".

I can likewise say 12 twelfths that a kilometres is 1 km, so 18 twelfths is 1 km and 6 twelfths the a km.

This I can write as (1frac612). It is the same as (1frac12)km.

Gertie was also asked the question: exactly how much is (4frac59 + 2frac79) ?

She thought favor this to answer it:

(4frac59) is 4 wholes and 5 ninths, and (2frac79) is 2 wholes and 7 ninths.

So altogether it is 6 wholes and 12 ninths. However 12 ninths is 9 ninths (1 whole) and 3 ninths, for this reason I can say it is 7 wholes and also 3 ninths.

I have the right to write (7frac39).

would certainly Gertie be wrong if she said her answer was (7frac13)?

Senthereng has (4frac712) party of food preparation oil. He offers (1frac512) bottles to his girlfriend Willem. Just how much oil does Senthereng have left?

Margaret has actually (5frac5 8 ) party of food preparation oil. She offers (3frac7 8) party to her friend Naledi. Exactly how much oil go Margaret have actually left?

calculation each that the following:

(4frac27 - 3frac67) (3frac67 + frac37) (3frac67 + 1frac45) (4frac38 - 2frac45) (1frac310 - frac23) (3frac510 - 1frac12) (frac58 + frac58 + frac58 + frac58 + frac58) (6frac25 + 2frac14 -frac12) (frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58 + frac58) (2frac47 + 2frac47 + 2frac47 + 2frac47 + 2frac47 + 2frac47 + 2frac47 + 2frac47) ((4frac27 + 1frac47) - 2frac13) ((2frac710 + 3frac35) - (1frac25 + 3frac710))

Neo"s report had five chapters. The very first chapter to be (frac3 4 ) that a page, the second chapter to be (2frac1 2 ) pages, the third chapter was (3frac3 4 ) pages, the fourth chapter to be 3 pages and the fifth chapter was (1frac1 2 ) pages. How many pages to be Neo"s report in total?

Tenths and hundredths (percentages)

100 kids each gain 3 biscuits. How numerous biscuits is this in total?

500 sweets are shared equally in between 100 children. How many sweets go each boy get?

The picture below mirrors a piece of licorice. The very small pieces can quickly be broken off top top the slim lines. How numerous very tiny pieces are shown on the picture?

Gatsha runs a spaza shop. That sells strips the licorice prefer the above for R2 each.

What is the expense of one very small piece the licorice, once you buy native Gatsha?

Jonathan wants to purchase one fifth of a piece of licorice. Just how much have to he pay?

Batseba eats 25 very little pieces. What part of a totality strip the licorice is this?

Each tiny piece the the over strip is one hundredth of the whole strip.

Why have the right to each little piece be referred to as one hundredth of the totality strip?

How many hundredths is the same as one tenth the the strip?

Gatsha frequently sells components of licorice strips come customers. He offers a "quarters marker" and a "fifths marker" to reduced off the pieces appropriately from complete strips. His 2 markers are shown below, alongside a complete strip that licorice.

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How plenty of hundredths is the exact same as 2 fifths the the whole strip?

How plenty of tenths is the exact same as (frac2 5 ) the the totality strip?

How countless hundredths is the very same as (frac3 4 ) of the totality strip?

Freddie purchase (frac60 100 ) the a strip. How many fifths of a strip is this?

Jamey bought component of a piece for R1,60. What component 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 below. Just how much (what part of a entirety strip) did every of them get?

The yellow licorice shown above costs R2,40 (240 cents) because that a strip. How much does each of the youngsters have to pay? Round turn off the quantities to the nearest cent.