Unit 6 — Fractions: Operations and Problem Solving

Welcome back!

Fractions help us describe parts of a whole.

We use fractions every day when measuring ingredients, dividing objects into equal parts, calculating time, and solving real-world problems.

Today you will strengthen your understanding of fractions by learning how to add, subtract, multiply, and divide them.

Reviewing Fractions

A fraction has two parts.

The numerator tells how many parts are being considered.

The denominator tells how many equal parts make up the whole.

Example:

3/5

• Numerator = 3
• Denominator = 5

Always remember that the denominator cannot be zero.

Equivalent Fractions

Equivalent fractions represent the same value.

Examples:

• 1/2 = 2/4
• 3/4 = 6/8
• 5/10 = 1/2

Multiply or divide both the numerator and denominator by the same nonzero number to create equivalent fractions.

Equivalent fractions are often needed before adding or subtracting fractions.

Adding and Subtracting Fractions

Fractions must have a common denominator before they can be added or subtracted.

Example:

1/4 + 2/4 = 3/4

If the denominators are different, first find a common denominator.

Then:

• add or subtract the numerators
• keep the common denominator
• simplify the answer if possible

Multiplying Fractions

To multiply fractions:

• multiply the numerators
• multiply the denominators
• simplify the result if possible

Example:

2/3 × 5/6

Multiply:

2 × 5 = 10

3 × 6 = 18

Simplify:

10/18 = 5/9

Dividing Fractions

To divide by a fraction:

1. Keep the first fraction.
2. Change division to multiplication.
3. Turn the second fraction upside down (find its reciprocal).
4. Multiply.
5. Simplify.

Example:

3/4 ÷ 2/5

becomes

3/4 × 5/2 = 15/8 = 1 7/8

Always simplify your final answer.

Mixed Numbers

A mixed number contains a whole number and a fraction.

Example:

2 3/4

Sometimes it is easier to convert mixed numbers to improper fractions before multiplying or dividing.

Example:

2 3/4 = 11/4

Converting between mixed numbers and improper fractions is an important Grade 5 skill.

Solving Word Problems

Fractions appear in many everyday situations.

Examples include:

• cooking recipes
• measuring distances
• sharing food
• construction projects
• science experiments

Read each problem carefully.

Identify:

• what is known
• what must be found
• which operation is needed

Estimate when possible, then solve carefully.

Activity

Solve:

• three addition problems
• three subtraction problems
• three multiplication problems
• three division problems

Then write one real-world word problem using fractions and solve it.

Explain each step of your reasoning.

Practice

Answer these questions.

What is an equivalent fraction?

Why do fractions need common denominators before adding or subtracting?

How do you multiply fractions?

What is the reciprocal of a fraction?

What is a mixed number?

Why should you simplify fractions?

Review

Today you learned:

• equivalent fractions represent the same value
• common denominators are needed for addition and subtraction
• multiplying fractions is straightforward when numerators and denominators are multiplied
• dividing fractions requires multiplying by the reciprocal
• mixed numbers and improper fractions can be converted back and forth
• fractions help solve many real-world problems

Mastering fractions prepares you for decimals, percentages, ratios, algebra, and many future mathematical concepts.

Looking Ahead

Next we will explore decimals in greater depth, learning how to perform operations with decimal numbers and apply them to money, measurement, science, and everyday problem solving.