Fractions and Decimals – Basic 6 Mathematics Lesson Note (First Term)

Addition and Subtraction of Fractions

Adding Fractions with Same Denominators

Rule: Add the numerators, keep the denominator

Example: 3/7 + 2/7 = (3+2)/7 = 5/7

Adding Fractions with Different Denominators

Steps:

1. Find the L.C.M of denominators
2. Convert to equivalent fractions
3. Add numerators
4. Simplify if possible

Example: 1/3 + 1/4

L.C.M of 3 and 4 = 12

1/3 = 4/12

1/4 = 3/12

4/12 + 3/12 = 7/12

Subtracting Fractions

Same method as addition, but subtract numerators

Example: 5/6 – 1/4

L.C.M of 6 and 4 = 12

5/6 = 10/12

1/4 = 3/12

10/12 – 3/12 = 7/12

Exercise A – Addition of Fractions

Solve these problems:

1. 2/5 + 1/5 = ______
2. 3/8 + 1/4 = ______
3. 1/3 + 1/6 = ______
4. 2/7 + 3/14 = ______
5. 5/12 + 1/4 + 1/3 = ______

Exercise B – Subtraction of Fractions

Solve these problems:

1. 4/5 – 1/5 = ______
2. 3/4 – 1/3 = ______
3. 5/6 – 1/2 = ______
4. 7/8 – 1/4 = ______
5. 11/12 – 1/3 = ______

Multiplication and Division of Fractions

Multiplying Fractions

Rule: Multiply numerators together, multiply denominators together

Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2

Multiplying by Whole Numbers

Example: 3/5 × 4 = (3×4)/5 = 12/5 = 2 2/5

Dividing Fractions

Rule: Multiply by the reciprocal (flip the second fraction)

Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9

Mixed Numbers

Convert to improper fractions first

Example: 2 1/3 × 1 1/4

2 1/3 = 7/3

1 1/4 = 5/4

7/3 × 5/4 = 35/12 = 2 11/12

Exercise C – Multiplication of Fractions

Solve these problems:

1. 1/2 × 1/3 = ______
2. 2/5 × 3/4 = ______
3. 3/8 × 4 = ______
4. 1 1/2 × 2/3 = ______
5. 2 1/4 × 1 1/3 = ______

Exercise D – Division of Fractions

Solve these problems:

1. 1/2 ÷ 1/4 = ______
2. 3/4 ÷ 1/2 = ______
3. 2/3 ÷ 4 = ______
4. 1 1/2 ÷ 3/4 = ______
5. 2 2/5 ÷ 1 1/5 = ______

Real Life Problems on Fractions

Food and Cooking

Example: Mama used 2/3 of a bag of rice for jollof rice and 1/4 of the bag for fried rice. What fraction of the bag did she use in total?

Solution: 2/3 + 1/4 = 8/12 + 3/12 = 11/12

Exercise E – Food Problems

Solve these problems:

1. Cake Sharing: A cake is cut into 8 equal pieces. If Tunde ate 3 pieces and Kemi ate 2 pieces, what fraction of the cake is left? Answer: ______
2. Cooking Ingredients: A recipe needs 2 1/2 cups of flour. If Mama has only 1 3/4 cups, how much more flour does she need? Answer: ______
3. Fruit Sharing: 3/4 of a watermelon was shared equally among 6 children. What fraction did each child get? Answer: ______

Exercise F – Money and Shopping

Solve these problems:

1. Pocket Money: Ade spent 2/5 of his pocket money on books and 1/4 on transport. What fraction of his money is left? Answer: ______
2. Savings: Folake saves 1/3 of her monthly allowance. If her allowance is ₦1,200, how much does she save? Answer: ₦______
3. Shopping: A trader sold 3/8 of her goods on Monday and 1/4 on Tuesday. If she had 240 items, how many items are left? Answer: ______

Exercise G – Time and Distance

Sol

ve these problems:

1. Journey Time: A journey takes 2 2/3 hours by car. How long will it take to complete 3/4 of the journey? Answer: ______ hours
2. Work Progress: Workers completed 5/8 of a road project in 15 days. At the same rate, how many days will they need to complete the whole project? Answer: ______ days
3. Sports Practice: A football practice session lasts 1 1/2 hours. If 2/3 of the time is spent on drills, how many minutes are spent on drills? Answer: ______ minutes

Quantitative Reasoning

Fraction to Decimal Conversion

Method: Divide numerator by denominator

Examples:

• 1/2 = 1 ÷ 2 = 0.5
• 3/4 = 3 ÷ 4 = 0.75
• 1/8 = 1 ÷ 8 = 0.125

Decimal to Fraction Conversion

Method: Write as fraction with appropriate denominator

Examples:

• 0.5 = 5/10 = 1/2
• 0.25 = 25/100 = 1/4
• 0.75 = 75/100 = 3/4

Exercise H – Fraction-Decimal Conversion

Convert these fractions to decimals:

1. 1/4 = ______
2. 3/5 = ______
3. 7/8 = ______
4. 2/3 = ______ (round to 3 decimal places)
5. 5/6 = ______ (round to 3 decimal places)

Exercise I – Decimal-Fraction Conversion

Convert these decimals to fractions in simplest form:

1. 0.2 = ______
2. 0.6 = ______
3. 0.125 = ______
4. 0.375 = ______
5. 0.4 = ______

Exercise J – Comparing Fractions

Use >, <, or = to compare:

1. 2/3 _____ 3/4
2. 5/8 _____ 0.6
3. 1/2 _____ 0.5
4. 3/5 _____ 7/10
5. 2/9 _____ 0.25

Exercise K – Fraction Patterns

Complete these patterns:

1. 1/2, 2/4, 3/6, _____, _____
2. 1/3, 2/6, 3/9, _____, _____
3. 0.1, 0.3, 0.5, _____, _____
4. 1/4, 1/2, 3/4, _____, _____

Exercise L – Word Problem Reasoning

Solve these challenging problems:

1. Class Performance: In a test, 1/4 of students got A, 2/5 got B, 1/6 got C, and the rest got D. What fraction got D? If there are 60 students, how many got each grade? Answer: Fraction D: ______ Numbers: A:____ B:____ C:____ D:____
2. Production Planning: A factory produces toys. On Monday, they made 2/7 of their weekly target. On Tuesday, they made 1/3 of the target. How much more do they need to complete their target? Answer: ______
3. Ingredient Calculation: A recipe for 4 people needs 3/4 cup of oil. How much oil is needed for 6 people? How much for 10 people? Answer: 6 people: ______ 10 people: ______

Answer Key

Exercise A:

1. 3/5
2. 5/8
3. 1/2
4. 1/2
5. 1

Exercise B:

1. 3/5
2. 5/12
3. 1/3
4. 5/8
5. 7/12

Exercise C:

1. 1/6
2. 6/20 = 3/10
3. 3/2 = 1 1/2
4. 1
5. 3

Exercise D:

1. 2
2. 1 1/2
3. 1/6
4. 2
5. 2

Exercise E:

1. 3/8
2. 3/4 cup
3. 1/8

Exercise F:

1. 7/20
2. ₦400
3. 90 items

Exercise G:

1. 2 hours
2. 24 days
3. 60 minutes

Exercise H:

1. 0.25
2. 0.6
3. 0.875
4. 0.667
5. 0.833

Exercise I:

1. 1/5
2. 3/5
3. 1/8
4. 3/8
5. 2/5

Exercise J:

1. <
2. =
3. <
4. <

Exercise L:

1. Fraction D: 13/60, A:15, B:24, C:10, D:13
2. 8/21
3. 6 people: 1 1/8 cups, 10 people: 1 7/8 cups