Adding and Subtracting Fractions

Grade 5 · Math · Study Guide

Learn how to add and subtract fractions with like and unlike denominators.

Fractions represent parts of a whole. When you add or subtract fractions, the process depends on whether the denominators are the same or different.

When fractions have the same denominator (like denominators), simply add or subtract the numerators and keep the denominator the same. For example, 3/8 + 2/8 = 5/8.

When fractions have different denominators (unlike denominators), you must first find a common denominator. The least common denominator (LCD) is the smallest number that both denominators divide into evenly. Rename each fraction as an equivalent fraction using the LCD, then add or subtract the numerators.

For example, to solve 1/3 + 1/4, the LCD is 12. Rename: 4/12 + 3/12 = 7/12.

Don't forget to simplify your answer! Divide both the numerator and denominator by their greatest common factor (GCF). A fraction is in simplest form when the only common factor of the numerator and denominator is 1.

For mixed numbers, add or subtract the whole number parts and the fraction parts separately. If the fraction part of the result is improper (numerator larger than denominator), convert it to a mixed number and add to the whole number.

Key terms

Numerator
The top number of a fraction that tells how many parts you have
Denominator
The bottom number of a fraction that tells how many equal parts make a whole
Least Common Denominator (LCD)
The smallest number that is a multiple of both denominators, used to rename fractions before adding or subtracting
Equivalent Fractions
Fractions that have the same value even though they look different, such as 1/2 and 2/4
Simplest Form
A fraction where the numerator and denominator share no common factor other than 1
Mixed Number
A number made up of a whole number and a proper fraction, such as 2 3/4

Flashcards

3/8 + 2/8
5/8 — same denominators, just add numerators
1/2 + 1/4
3/4 — LCD is 4; rename 1/2 as 2/4, then 2/4 + 1/4 = 3/4
5/6 - 1/3
1/2 — LCD is 6; rename 1/3 as 2/6, then 5/6 - 2/6 = 3/6 = 1/2
Equivalent fraction for 2/3 with denominator 12
8/12 — multiply numerator and denominator by 4
Mixed number for 9/4
2 1/4 — 4 goes into 9 twice with 1 left over
Simplest form of 4/8
1/2 — divide numerator and denominator by GCF of 4
1/3 + 1/4
7/12 — LCD is 12; rename as 4/12 + 3/12 = 7/12
3/4 - 1/6
7/12 — LCD is 12; rename as 9/12 - 2/12 = 7/12

Questions

  1. What is 2/5 + 1/5?

    1. 3/10
    2. 3/5
    3. 2/5
    4. 1/5
    Show answer

    Answer: 3/5

    When denominators are the same, add the numerators: 2 + 1 = 3, keep the denominator 5, giving 3/5.

  2. To add 1/3 + 1/4, you can add the numerators and add the denominators to get 2/7.

    Show answer

    Answer: False

    You cannot add denominators. You must find the LCD (12), rename the fractions as 4/12 and 3/12, then add to get 7/12.

  3. The least common denominator of 1/4 and 1/6 is ___.

    Show answer

    Answer: 12

    Multiples of 4 are 4, 8, 12... and multiples of 6 are 6, 12... The smallest shared multiple is 12.

  4. What is 3/4 - 1/4?

    1. 2/8
    2. 2/4
    3. 1/2
    4. Both B and C
    Show answer

    Answer: Both B and C

    3/4 - 1/4 = 2/4, which simplifies to 1/2 by dividing both parts by 2. Both B (2/4) and C (1/2) are correct.

  5. 1/2 + 1/3 = ___ (write as a fraction in simplest form).

    Show answer

    Answer: 5/6

    LCD of 2 and 3 is 6. Rename: 3/6 + 2/6 = 5/6. Since 5 and 6 share no common factor, it is already in simplest form.

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