smc-4460-30-Add/Subtract fractions

Fractions, SM-Bank 058

Evaluate the following number sentences, giving your answers in simplest form.

`2 3/7-1 2/7` (1 mark)

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`3 1/2-1 3/5` (2 marks)

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`4 1/4-3 1/2` (2 marks)

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Show Answers Only

a. `1 1/7`

b. `1 9/10`

c. `3/4`

Show Worked Solution

a. `2 3/7-1 2/7`	`=1 3/7 -2/7`
	`= 1 1/7`

b. `3 1/2-1 3/5`	`=3 5/10-1 6/10`
	`= 2 5/10-6/10`
	`=1 9/10`

c. `4 1/4-3 1/2`	`=1 1/4-1/2`
	`= 1 1/4-2/4`
	`=3/4`

Fractions, SM-Bank 056

Sally makes bird feeders to hang in her garden.

The table below shows the fraction of the bird feeder eaten each day by the birds.

\begin{array} {|l|c|c|}
\hline \textbf{Day} & \textbf{Fraction Eaten} \\
\hline \text{Monday} & 3/10\\
\hline \text{Tuesday} & 1/5 \\
\hline \text{Wednesday} & 1/4 \\
\hline \text{Thursday} & ? \\
\hline \end{array}

If the whole feeder was consumed in four days, what fraction did the birds eat on Thursday? (2 marks)

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The bird feeder weighs 5 kilograms. How many kilograms were consumed on Monday? (2 marks)

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Show Answers Only

a. `1/4`

b. `1 1/2\ text(kilograms)`

Show Worked Solution

a. `text(Eaten Thursday)`	`= 1-(3/10+1/5+1/4)`
	`= 1-(6/20+4/20+5/20)`
	`= 1-15/20`
	`=5/20=1/4`

b. `text(Monday Kilograms)`	`= 3/10 xx 5`
	`= 15/10`
	`= 1 1/2\ text(kilograms)`

Fractions, SM-Bank 055

Evaluate the following number sentences, giving your answers in simplest form.

`1/6-5/6` (1 mark)

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`4/9-1/2` (2 marks)

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`-3/4-1/2` (2 marks)

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Show Answers Only

a. `-2/3`

b. `-1/18`

c. `-1 1/4`

Show Worked Solution

a. `1/6-5/6`	`=-4/6`
	`= -2/3`

b. `4/9-1/2`	`=(4 xx 2)/(9 xx 2)-(1 xx 9)/(2 xx 9)`
	`= 8/18-9/18`
	`=-1/18`

c. `-3/4-1/2`	`=-3/4-2/4`
	`= -5/4`
	`=-1 1/4`

Fractions, SM-Bank 054

Evaluate the following number sentences, giving your answers in simplest form.

`7/12-1/4` (1 mark)

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`3/5-2/7` (2 marks)

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`1/2-4/9` (2 marks)

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Show Answers Only

a. `1/3`

b. `11/35`

c. `1/18`

Show Worked Solution

a. `7/12-1/4`	`=7/12- (1 xx 3)/(4 xx 3)`
	`= 7/12-3/12`
	`=1/3`

b. `3/5-2/7`	`=(3 xx 7)/(5 xx 7)- (2 xx 5)/(7 xx 5)`
	`= 21/35-10/35`
	`=11/35`

c. `1/2-4/9`	`=(1 xx 9)/(2 xx 9)- (4 xx 2)/(9 xx 2)`
	`= 9/18-8/18`
	`=1/18`

Fractions, SM-Bank 053

What is the difference between `4/5` and `3/4`? (2 marks)

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Show Answers Only

`1/20`

Show Worked Solution

`text(Difference)`	`= 4/5-3/4`
	`= (4 xx 4)/(5 xx 4)-(3 xx 5)/(4 xx 5)`
	`=16/20-15/20`
	`=1/20`

Fractions, SM-Bank 052 MC

What is the difference between `5/8` and `1/4`?

`1`
`4/8`
`1/2`
`3/8`

Show Answers Only

`D`

Show Worked Solution

`text(Difference)`	`=5/8-1/4`
	`= 5/8-2/8`
	`= 3/8`

`=> D`

Fractions, SM-Bank 050 MC

A walking path near the beach is paved for half of the length, cobbled stone for `3/10` of the length and then grass for the rest of the path.

For what fraction of the path is it grass?

`1/5`
`3/10`
`3/5`
`8/10`

Show Answers Only

`A`

Show Worked Solution

`text(Fraction of the path that is grass)`

`=1-(1/2 + 3/10)`

`=1-8/10`

`=2/10=1/5`

`=>A`

Fractions, SM-Bank 49 MC

A garden centre sells a potting mix made up of soil, manure and sand.

Soil makes up `3/4` of the mix and manure makes up `1/6` of the mix.

What fraction of the potting mix is sand?

`1/12`
`1/40`
`5/12`
`3/7`

Show Answers Only

`D`

Show Worked Solution

`text(Sand)`	`= 1-(3/4 + 1/6)`
	`= 1-(9/12 + 2/12)`
	`= 1/12`

`=> D`

Fractions, SM-Bank 048

George has 5 cups of gluten free flour.

He uses `2 1/2` cups of gluten free flour for one recipe and gives `3/4` cup to a friend.

How many cups of gluten free flour does George have left? (2 marks)

Show Answers Only

`1 3/4`

Show Worked Solution

`text(Cups used) = 2 1/2 + 3/4 = 3 1/4`

`text(Cups left)`	`= 5-3 1/4`
	`= 2-1/4`
	`= 1 3/4`

Fractions, SM-Bank 045 MC

`+ 7/8 = 23/8`

What value makes this number sentence correct?

`16`
`3 2/7`
`2 7/8`
`2`

Show Answers Only

`D`

Show Worked Solution

	`+ 7/8`	`= 23/8`
		`= 23/8-7/8`
		`= 16/8`
		`= 2`

`=> D`

Fractions, SM-Bank 044

Add the following mixed numbers giving your answer in simplest form.

`2 5/8 + 1 3/4` (2 mark)

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`4 5/6 + 3 4/9` (2 mark)

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`1 3/5 + 5 2/3 + 4 7/10` (2 marks)

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Show Answers Only

a. `4 3/8`

b. `8 5/18`

c. `11 29/30`

Show Worked Solution

a. Method: Adding whole number parts first

	`2 5/8+1 3/4`	`=2 + 1 + 5/8 + 3/4\ \ \ text(LCD)\= 8`
		`= 3 + 5/8 + 6/8`
		` = 3 + 11/8 = 4 3/8`

b. Method: Adding whole number parts first

	`4 5/6 +3 4/9`	`=4 + 3 + 5/6 + 4/9\ \ \ text(LCD)\= 18`
		`= 7 + (5 xx 3)/(6 xx 3) + (4 xx 2)/(9 xx 2)`
		` = 7 + 15/18 + 8/18`
		`= 7 + 23/18 = 8 5/18`

c. Method: Adding whole number parts first

	`1 3/5+5 2/3+4 7/10`	`=1 + 5 + 4 +3/5 +2/3+7/10\ \ \ text(LCD)\= 30`
		`= 10 + (3 xx 6)/(5 xx 6) + (2 xx 10)/(3 xx 10) + (7 xx 3)/(10 xx 3)`
		` = 10 + 18/30 + 20/30 + 21/30`
		`= 10 + 59/30 = 11 29/30`

Fractions, SM-Bank 043

Add the following mixed numbers giving your answer in simplest form.

`1 1/3 + 1 2/3` (1 mark)

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`2 4/9 + 1 2/9` (2 mark)

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`1 1/11 + 2 5/11 + 4 7/11` (2 marks)

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Show Answers Only

a. `3`

b. `3 2/3`

c. `8 2/11`

Show Worked Solution

a. Method 1: Adding whole number parts first

	`1 1/3+1 2/3`	`=1 + 1 +1/3 + 2/3`
		`= 2 + 3/3`
		` = 3`

Method 2: Changing to improper fractions

	`1 1/3+1 2/3`	`=(3 xx 1 + 1)/3 + (3 xx 1 + 2)/3`
		`= 4/3 + 5/3`
		` = 9/3 = 3`

b. Method 1: Adding whole number parts first

	`2 4/9 +1 2/9`	`=2 + 1 +4/9 + 2/9`
		`= 3 + 6/9`
		` = 3 2/3`

Method 2: Changing to improper fractions

	`2 4/9 +1 2/9`	`=(2 xx 9 + 4)/9 + (1 xx 9 + 2)/9`
		`= 22/9 + 11/9`
		` = 33/9 `
		`= 3 6/9 = 3 2/3`

c. Method 1: Adding whole number parts first

	`1 1/11+2 5/11+4 7/11`	`=1 + 2 + 4 +1/11 +5/11+7/11`
		`= 7 + 13/11`
		` = 8 2/11`

Method 2: Changing to improper fractions

	`1 1/11+2 5/11+4 7/11`	`=(1 xx 11 + 1)/11 +(2 xx 11 + 5)/11 + (4 xx 11 + 7)/11 +`
		`= 12/11 + 27/11+51/11`
		` = 90/11 = 8 2/11`

Fractions, SM-Bank 042

Add the following fractions giving your answer in simplest form.

`1/3 + 1/4` (1 mark)

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`3/10 + 1/5` (2 mark)

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`1/2 + 1/3 + 1/8` (2 marks)

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Show Answers Only

a. `7/12`

b. `1/2`

c. `23/24`

Show Worked Solution

a.	`1/3+1/4`	`= (1xx4)/(3 xx 4) + (1 xx 3)/(4 xx 3)\ \ \ text(LCD)\= 12`
		`= 4/12 + 3/12`
		` = 7/12`

b.	`3/10 +1/5`	`= 3/10 + (1 xx 2)/(5 xx 2)\ \ \ text(LCD)\= 10`
		`= 3/10 + 2/10`
		` = 5/10 = 1/2`

c.	`1/2 +1/3 + 1/8`	`= (1 xx 12)/(2 xx 12) + (1 xx 8)/(3 xx 8) + (1 xx 3)/(8 xx 3)\ \ \ text(LCD)\= 24`
		`= 12/24 + 8/24 + 3/24`
		` = 23/24`

Fractions, SM-Bank 041

Add the following fractions giving your answer as a mixed number where necessary.

`4/9 + 1/9` (1 mark)

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`5/7 + 6/7` (1 mark)

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`2/15 + 7/15 + 8/15` (2 marks)

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Show Answers Only

a. `5/9`

b. `1 4/7`

c. `1 2/15`

Show Worked Solution

a. `4/9 + 1/9 = 5/9`

b. `5/7 + 6/7 = 11/7 = 1 4/7`

c. `2/15 + 7/15 + 8/15 = 17/15 = 1 2/15`

Fractions, SM-Bank 040

Three friends are baking cupcakes for the Spring Fair.

Maryanne will bake `1/4` of the cupcakes, Martin has a large oven and will bake `2/3` of the cupcakes and Monty will bake the rest.

What fraction of the cupcake baking does Monty complete? (2 marks)

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Show Answers Only

`1/12`

Show Worked Solution

`text(Monty’s Baking)`

`= 1-(1/4 + 2/3)\ \ text(LCD)\= 12`

`= (1xx12)/(1 xx 12)-((1xx3)/(4 xx 3) + (2 xx 4)/(3 xx 4))`

`= 12/12-(3/12 + 8/12)`

`= 12/12-11/12 = 1/12`

`:.\ text(Monty bakes)\ 1/12\ text(of the cupcakes)`

Fractions, SM-Bank 039

Three friends are running as a team in a fun run.

Thanh hopes to finish `3/7` of the run, Jamieson is confident he can complete `1/2` of the run and Jules will complete the rest.

What fraction of the fun run does Jules complete? (2 marks)

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Show Answers Only

`1/14`

Show Worked Solution

`text(Jules)`

`= 1-(3/7 + 1/2)\ \ text(LCD)\= 14`

`= (1xx14)/(1 xx 14)-((3xx2)/(7 xx 2) + (1 xx 7)/(2 xx 7))`

`= 14/14-(6/14 + 7/14)`

`= 14/14-13/14 = 1/14`

`:.\ text(Jules completes)\ 1/14\ text(of the race)`

Fractions, SM_Bank 038

What is the lowest common denomiator of the following sets of fractions?

`1/4, 1/8` (1 mark)

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`2/3, 4/5` (1 mark)

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`1/2, 2/3, 1/6` (1 mark)

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`1/9, 5/6, 7/12` (1 mark)
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Show Answers Only

a. `8`

b. `15`

c. `6`

d. `36`

Show Worked Solution

a. `text(8 is the lowest number that is a multiple of both 4 and 8)`

`:.\ text(LCD) (1/4, 1/8) = 8`

b. `text(15 is the lowest number that is a multiple of both 3 and 5)`

`:.\ text(LCD) (2/3, 4/5)= 15`

c. `text(6 is the lowest number that is a multiple of 2, 3 and 6)`

`:.\ text(LCD) (1/2, 2/3, 1/6) = 6`

d. `text(36 is the lowest number that is a multiple of 9, 6 and 12)`

`:.\ text(LCD) (1/9, 5/6, 7/12) = 36`

Fractions, SM-Bank 037

What is the lowest common multiple of the following sets of numbers?

`2, 5` (1 mark)

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`3, 9` (1 mark)

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`2, 3, 6` (1 mark)

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`4, 6, 8` (1 mark)
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Show Answers Only

a. `10`

b. `9`

c. `6`

d. `24`

Show Worked Solution

a. `text(Multiples of 2:)\ 2, 4, 6, 8, 10`

`text(Multiples of 5:)\ 5, 10`

`:.\ text(LCM (2, 5))= 10`

b. `text(Multiples of 3:)\ 3, 6, 9`

`text(Multiples of 9:)\ 9`

`:.\ text(LCM (3, 9))= 9`

c. `text(Multiples of 2:)\ 2, 4, 6`

`text(Multiples of 3:)\ 3, 6`

`text(Multiples of 6:)\ 6`

`:.\ text(LCM (2, 3, 6))= 6`

d. `text(Multiples of 4:)\ 4, 8, 12, 16, 20, 24`

`text(Multiples of 6:)\ 6, 12, 18, 24`

`text(Multiples of 8:)\ 8, 16, 24`

`:.\ text(LCM (4, 6, 8))= 24`

Fractions, SM-Bank 036

Jaime and Jordan ordered 2 extra large pizzas for dinner.

Jaime ate `2/5` of an extra large pizza.

If Jordan ate 3 times as much pizza as Jaime, how much pizza did Jordan eat? Give your answer as a mixed number. (1 mark)

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What fraction of pizza is left over? (2 marks)

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Show Answers Only

a. `1 1/5\ text(pizzas)`

b. `2/5\ text(of a pizza)`

Show Worked Solution

a. `text(Jordan’s Pizza)`

`= 3 xx 2/5`

`= 6/5`

`= 1 1/5\ text(pizzas)`

b. `text(Leftover pizza)`

`= 2-(2/5 + 1 1/5)`

`= 2-1 3/5`

`= 2/5\ text(of a pizza)`

Fractions, SM-Bank 007 MC

The fraction `8/10` and `1/5` have been shaded on this fraction wall.

What is `8/10 - 1/5?`

`7/5`
`7/10`
`6/10`
`8/10`

Show Answers Only

`C`

Show Worked Solution

`text(The fraction wall can be used to graphically)`

`text(see the difference as)\ \ 6/10.`

`text(Alternatively,)`

`8/10 – 1/5`	`= 8/10 – 2/10`
	`= 6/10`

`=> C`

Fractions, SM-Bank 004

Which number is exactly halfway between `1 1/3` and `4 2/3`? (2 marks)

Show Answers Only

`3`

Show Worked Solution

`text(Halfway)`	`= (1 1/3 + 4 2/3) ÷ 2`
	`= 6 ÷ 2`
	`= 3`

`text(Raisins needed)`	`= 3/4-3/8`
	`=6/8-3/8`
	` =3/8\ text(cup)`