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1. Fractions

Fractions are a way to represent parts of a whole number or mixed numbers. They are denoted by using a numerator and denominator. To add or subtract fractions, the denominators of the fractions must be made the same by multiplying the numerator and denominator by the same number to create equivalent fractions like, for instance, ²/₈ and ¹/₄. To multiply fractions, find the product of their numerators and of their denominators. And to divide fractions, multiply a fraction with the inverse of the dividing fraction. # 1

Express ¹²/₇ as a mixed number.

7 goes into 12 fully only once, therefore the whole number part of the mixed number is 1.
The remainder is 5, so the fraction part of the mixed number will be 5/7.
Putting this together gives 1 ⁵/₇.

1 ⁵/₇ # 2

Lester is conducting an experiment in his science lesson. He finds that adding 100 ml of vegetable oil to 10 ml of sodium hydroxide produces 10 g of soap and he has 1 litre of vegetable oil and 120 ml of sodium hydroxide available to make as much soap as he can. Find how much of sodium hydroxide Lester needs out of the total amount he has.

¹⁰⁰/₁₂₀ = ⁵/₆

⁵/₆ # 3

Find the difference between ⁵/₇ and ³/₁₄.

⁵/₇ − ³/₁₄ = ¹⁰/₁₄ − ³/₁₄ = ⁷/₁₄ = ¹/₂

¹/₂ # 4

Simplify 7 + ⁷/₄ and express your answer as a mixed number.

7 + ⁷/₄ = ²⁸/₄ + ⁷/₄ = ³⁵/₄ = 8 ³/₄

8 ³/₄ # 5

Calculate 2 ÷ ²/₅.

2 ÷ ²/₅ = ²/₁ × ⁵/₂ = 5

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