smc-4460-15-Simplifying Fractions

Fractions, SM-Bank 070

Write reciprocals for the following.

`4/5` (1 mark)

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`3` (1 mark)

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`1 3/4` (2 marks)

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a. `5/4`

b. `1/3`

c. `4/7`

Show Worked Solution

a. `5/4`

`=> 4/5\ \ \ \ text{(Swap the numerator and denominator)}`

b. `3`	`= 3/1\ \ \ \ text{(Write whole numbers as fractions with a denominator of 1)}`
	`=> 1/3\ \ \ \ text{(Then swap the numerator and denominator)}`

c. `1 3/4`	`= 7/4 \ \ \ \ text{(Change mixed numbers to improper fractions)}`
	`=> 4/7 \ \ \ \ text{(Then swap the numerator and denominator)}`

Fractions, SM-Bank 033

Which two of the following fractions are not in simplest form? (2 marks)

`1/3, 2/9, 5/15, 6/28, 8/21`

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`5/15, 6/28`

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`5/15 = 1/3\ text(and)\ 6/28 = 3/14`

`:.\ 5/15\ text(and)\ 6/28\ text(not in simplest form.)`

Fractions, SM-Bank 032

Which two of the following fractions are not in simplest form? (2 marks)

`1/8, 3/7, 4/12, 9/11, 7/14`

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`4/12, 7/14`

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`4/12 = 1/3\ text(and)\ 7/14 = 1/2`

`:.\ 4/12\ text(and)\ 7/14\ text(not in simplest form.)`

Fractions, SM-Bank 031

Convert `\ 7 9/11` to an improper fraction. (1 mark)

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`86/11`

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`7 9/11`	`= (7 xx 11 + 9)/11`
	`=86/11`

Fractions, SM-Bank 030

Convert `8 5/9` to an improper fraction. (1 mark)

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`77/9`

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`8 5/9`	`= (8 xx 9 + 5)/9`
	`=77/9`

Fractions, SM-Bank 029

Convert `4 1/5` to an improper fraction. (1 mark)

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`21/5`

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`4 1/5`	`= (4 xx 5 + 1)/5`
	`=21/5`

Fractions, SM-Bank 028

Convert `99/12` to a mixed number, in simplest form. (2 marks)

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`8 1/4`

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`99/12`	`= 99÷12`
	`= 8\ text(remainder)\ 3`

`:.\ 99/12 = 8 3/12 = 8 1/4\ text{(in simplest form)}`

Fractions, SM-Bank 027

Convert `35/14` to a mixed number, in simplest form. (2 marks)

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`2 1/2`

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`35/14`	`= 35÷14`
	`= 2\ text(remainder)\ 7`

`:.\ 35/14 = 2 7/14 = 2 1/2\ text{(in simplest form)}`

Fractions, SM-Bank 026

Convert `84/40` to a mixed number, in simplest form. (2 marks)

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`2 1/10`

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`84/40`	`= 84÷40`
	`= 2\ text(remainder)\ 4`

`:.\ 84/40 = 2 4/40 = 2 1/10\ text{(in simplest form)}`

Fractions, SM-Bank 025

Convert `47/7` to a mixed number. (1 mark)

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`6 5/7`

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`47/7`	`= 47÷7`
	`= 6\ text(remainder)\ 5`

`:.\ 47/7 = 6 5/7`

Fractions, SM-Bank 024

Convert `27/5` to a mixed number. (1 mark)

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`5 2/5`

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`27/5`	`= 27÷5`
	`= 5\ text(remainder)\ 2`

`:.\ 27/5 = 5 2/5`

Fractions, SM-Bank 023

Convert `11/7` to a mixed number. (1 mark)

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`1 4/7`

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`11/7`	`= 11÷7`
	`= 1\ text(remainder)\ 4`

`:.\ 11/7 = 1 4/7`

Fractions, SM-Bank 022

Simplify `896/1248`, giving your answer in simplest form. (2 marks)

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`28/39`

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`text(Note: when there are too many factors to list, divide by known common factors.)`

`896/1248`	`= (896÷4)/(1248÷4) `
	`= 224/312`
	`= (224÷4)/(312÷4)`
	`= 56/78`
	`= (56÷2)/(78÷2)`
	`=28/39`

`:.\ 896/1248 = 28/39\ text(in simplest form)`

Fractions, SM-Bank 021

Simplify `2550/5000`, giving your answer in simplest form. (2 marks)

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`51/100`

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`text(Note: when there are too many factors to list, divide by known common factors.)`

`2550/5000`	`= (2550÷10)/(5000÷10) `
	`= 255/500`
	`= (255÷5)/(500÷5)`
	`= 51/100`

`:.\ 2550/5000 = 51/100\ text(in simplest form)`

Fractions, SM-Bank 020

Simplify `27/45`, giving your answer in simplest form. (1 mark)

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`3/5`

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`text(Factors 27:)\ 1, 3, 9, 27`

`text(Factors 45:)\ 1, 3, 5, 9, 15, 45`

`text(HCF)\ = 9`

`:.\ 27/45 = (27÷9)/(45÷9) = 3/5`

Fractions, SM-Bank 019

Simplify `25/75`, giving your answer in simplest form. (1 mark)

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`1/3`

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`text(Factors 25:)\ 1, 5, 25`

`text(Factors 75:)\ 1, 3, 5, 15, 25, 75`

`text(HCF)\ = 25`

`:.\ 25/75 = (25÷25)/(75÷25) = 1/3`

Fractions, SM-Bank 018

List all factors of 20 and 36. (2 marks)

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What is the highest common factor (HCF) of 20 and 36? (1 mark)

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Use the HCF of 20 and 36 to simplify `20/36`. (1 mark)

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a. `text(Factors of)\ 20: 1, 2, 4, 5, 10, 20`

`text(Factors of)\ 36: 1, 2, 3, 4, 6, 9, 12, 16, 36`

b. `text(HCF) = 4`

c. `20/36 = (20 ÷ 4)/(36 ÷ 4) = 5/9`

Show Worked Solution

a. `text(Factors of)\ 20: 1, 2, 4, 5, 10, 20`

`text(Factors of)\ 36: 1, 2, 3, 4, 6, 9, 12, 16, 36`

b. `text(Common Factors:)\ 1, 2, 4`

`text(HCF) = 4`

c. `text(To simplify, divide the numerator and denominator by HCF.)`

`20/36 = (20 ÷ 4)/(36 ÷ 4) = 5/9`