Class 5 — Mathematics

Fractions: Addition/Subtraction of Unlike Fractions and Multiplication of Fractions

Class 5

✓Identify unlike fractions and understand the need for a common denominator.
✓Add and subtract unlike fractions by finding their Least Common Multiple (L.C.M.) to make them equivalent fractions.
✓Multiply a fraction by a whole number.
✓Multiply a fraction by another fraction (proper or improper).
✓Simplify the resulting fractions to their lowest terms.

Key concepts

Unlike Fractions

Fractions that have different denominators are called unlike fractions. For example, 1/2 and 1/3 are unlike fractions because their denominators (2 and 3) are different.

Equivalent Fractions

Equivalent fractions are fractions that represent the same value, even though they look different. For example, 1/2 and 2/4 are equivalent fractions. We find equivalent fractions by multiplying the numerator and denominator by the same non-zero number.

Addition of Unlike Fractions

To add unlike fractions, we first need to convert them into equivalent fractions with the same denominator. This common denominator is usually the Least Common Multiple (L.C.M.) of the original denominators.\nSteps:\n1. Find the L.C.M. of the denominators.\n2. Convert each fraction into an equivalent fraction with the L.C.M. as the new denominator.\n3. Add the numerators of the equivalent fractions.\n4. Keep the common denominator.\n5. Simplify the resulting fraction to its lowest terms, if possible.

Subtraction of Unlike Fractions

To subtract unlike fractions, the process is similar to addition. We must first convert them into equivalent fractions with a common denominator (L.C.M.).\nSteps:\n1. Find the L.C.M. of the denominators.\n2. Convert each fraction into an equivalent fraction with the L.C.M. as the new denominator.\n3. Subtract the numerators of the equivalent fractions.\n4. Keep the common denominator.\n5. Simplify the resulting fraction to its lowest terms, if possible.

Multiplication of Fractions

To multiply fractions, we simply multiply the numerators together and multiply the denominators together.\nSteps:\n1. Multiply the numerators.\n2. Multiply the denominators.\n3. Write the product as a new fraction.\n4. Simplify the resulting fraction to its lowest terms, if possible.\nIf multiplying a fraction by a whole number, write the whole number as a fraction with denominator 1 (e.g., 5 as 5/1).\nIf multiplying mixed fractions, first convert them into improper fractions.

(a/b) × (c/d) = (a × c) / (b × d)

Key facts to remember

1Unlike fractions have different denominators.
2To add or subtract unlike fractions, first find the L.C.M. of their denominators.
3Convert unlike fractions into equivalent fractions with the L.C.M. as the common denominator.
4When adding or subtracting fractions, only the numerators are added or subtracted; the denominator remains the same.
5To multiply fractions, multiply the numerators together and multiply the denominators together.
6When multiplying a fraction by a whole number, treat the whole number as a fraction with a denominator of 1.
7Always simplify your final answer to its lowest terms.
8If the answer is an improper fraction, convert it to a mixed fraction.

Worked examples

Example 1

Add: 2/3 + 1/4

IThe denominators are 3 and 4. They are unlike fractions.

IIFind the L.C.M. of 3 and 4. The L.C.M. of 3 and 4 is 12.

IIIConvert 2/3 to an equivalent fraction with denominator 12: (2 × 4) / (3 × 4) = 8/12.

IVConvert 1/4 to an equivalent fraction with denominator 12: (1 × 3) / (4 × 3) = 3/12.

VNow add the equivalent fractions: 8/12 + 3/12 = (8 + 3) / 12 = 11/12.

VIThe fraction 11/12 is already in its lowest terms.

Answer

11/12

Example 2

Subtract: 5/6 - 1/3

IThe denominators are 6 and 3. They are unlike fractions.

IIFind the L.C.M. of 6 and 3. The L.C.M. of 6 and 3 is 6.

IIIThe fraction 5/6 already has the denominator 6.

IVConvert 1/3 to an equivalent fraction with denominator 6: (1 × 2) / (3 × 2) = 2/6.

VNow subtract the equivalent fractions: 5/6 - 2/6 = (5 - 2) / 6 = 3/6.

VISimplify the resulting fraction: 3/6 = (3 ÷ 3) / (6 ÷ 3) = 1/2.

Answer

1/2

Always simplify your answer to the lowest terms.

Example 3

Multiply: 3/5 × 2/7

IMultiply the numerators: 3 × 2 = 6.

IIMultiply the denominators: 5 × 7 = 35.

IIIWrite the product as a new fraction: 6/35.

IVCheck if 6/35 can be simplified. The common factors of 6 are 1, 2, 3, 6. The common factors of 35 are 1, 5, 7, 35. There are no common factors other than 1, so it is in its lowest terms.

Answer

6/35

Example 4

Multiply: 4 × 3/8

IWrite the whole number 4 as a fraction: 4/1.

IINow multiply the fractions: 4/1 × 3/8.

IIIMultiply the numerators: 4 × 3 = 12.

IVMultiply the denominators: 1 × 8 = 8.

VThe product is 12/8.

VISimplify the fraction 12/8. Both 12 and 8 are divisible by 4. (12 ÷ 4) / (8 ÷ 4) = 3/2.

VIIThis is an improper fraction. We can convert it to a mixed fraction: 3 ÷ 2 = 1 with a remainder of 1. So, 3/2 = 1 1/2.

Answer

1 1/2

Remember to convert whole numbers to fractions (e.g., 4 = 4/1) before multiplying.

Common mistakes

✗Adding or subtracting the denominators when adding or subtracting fractions (e.g., 1/2 + 1/3 = 2/5, which is incorrect).
✗Not finding the L.C.M. correctly, leading to incorrect equivalent fractions.
✗Forgetting to convert mixed fractions to improper fractions before multiplying.
✗Not simplifying the final answer to its lowest terms.
✗Making calculation errors when finding equivalent fractions or performing multiplication.

Exam tips

★Always show all your steps clearly, especially when finding the L.C.M. and converting to equivalent fractions.
★Double-check your L.C.M. calculations to avoid errors in subsequent steps.
★After performing addition, subtraction, or multiplication, always look for common factors in the numerator and denominator to simplify the fraction.
★If the question involves mixed fractions, convert them to improper fractions first for easier calculation, especially in multiplication.

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