## How to Add and Subtract Rational Numbers

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Rational numbers, forming a core classification of numbers, include values that can be denoted as a distinct ratio of two integers. In this piece, we're going to delve into the mechanics of adding and subtracting these rational numbers.

An **Easy-to-Follow Tutorial** on **Adding and Subtracting Rational Numbers**

Let's dive into the step-by-step process of adding and subtracting rational numbers:

**Phase 1:** Understanding Rational Numbers

Kickstarting our numerical journey, the first stage calls for a clear comprehension of rational numbers. Essentially, a rational number can be defined as a value expressible as a fraction, with both the numerator and the denominator being integers, and the denominator being non-zero.

**Phase 2:** Appreciating the Concept of Common Denominators

Building upon the foundational knowledge, the next step is grasping an important mathematical tenet: for adding or subtracting fractions, the denominators need to be identical, or 'common'. If the denominators differ, the fractions can't be directly combined or subtracted.

**Phase 3: **Creating Common Denominators

If the denominators are unlike, it's necessary to tweak the fractions to have common denominators. This can be done by finding the least common multiple (LCM) of the denominators and subsequently adjusting the fractions.

**Phase 4:** Modifying the Numerators

When changing fractions to have common denominators, it's important to similarly adjust the numerators. If you multiply or divide the denominator of a fraction, the numerator must be treated likewise. This maintains the fraction's value, despite its altered appearance.

**Phase 5:** Executing the Addition or Subtraction

With the fractions now sharing common denominators, the addition or subtraction can be carried out. In case of addition, merge the numerators and place the result over the common denominator. For subtraction, deduct the second numerator from the first and place the result over the common denominator.

### Exercises for Add or Subtract Rational Numbers

**1)** \({7 \over 4} \ + \ {5 \over 6} = \)

**2) **\({8 \over 10} \ + \ {2 \over 3} = \)

**3) **\({9 \over 8} \ + \ {8 \over 2} = \)

**4) **\({5 \over 3} \ - \ {3 \over 5} = \)

**5) **\({6 \over 3} \ - \ {8 \over 8} = \)

**6) **\({5 \over 1} \ - \ {5 \over 4} = \)

**7) **\({3 \over 2} \ - \ {7 \over 8} = \)

**8) **\({9 \over 3} \ - \ {3 \over 5} = \)

**9) **\({7 \over 11} \ + \ {16 \over 17} = \)

**10) **\({8 \over 9} \ + \ {15 \over 10} = \)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({7 \over 4} \ + \ {5 \over 6} = \)\( \ {7 \times 6 \ + \ 5 \times 4 \over 4\times6} =\)\({62 \over 24}\)

Then, simplify the result. \({62 \over 24} = {31 \over 12}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({8 \over 10} \ + \ {2 \over 3} = \)\( \ {8 \times 3 \ + \ 2 \times 10 \over 10\times3} =\) = \( {44 \over 30}\)

Then, simplify the result. \({44 \over 30} = {22 \over 15}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({9 \over 8} \ + \ {8 \over 2} = \)\( \ {9 \times 2 \ + \ 8 \times 8 \over 8\times2} =\)\({82 \over 16}\)

Then, simplify the result. \({82 \over 16} = {41 \over 8}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({5 \over 3} \ - \ {3 \over 5} = \)\( \ {5 \times 5 \ - \ 5 \times 3 \over 3\times5} = \)\({15 \over 10}\)

Then, simplify the result. \({2 \over 3} = 1\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({6 \over 3} \ - \ {8 \over 8} = \)\( \ {6 \times 8 \ - \ 8 \times 3 \over 3\times8} = \)\({24 \over 24}\)

Then, simplify the result. \({15 \over 15} = 1\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({5 \over 1} \ - \ {5 \over 4} = \)\( \ {5 \times 4 \ - \ 5 \times 1 \over 1\times4} = \)\({15 \over 4}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({3 \over 2} \ - \ {7 \over 8} = \)\( \ {3 \times 8 \ - \ 7 \times 2 \over 2\times8} = \)\({10 \over 16}\)

Then, simplify the result. \({10 \over 16} = { 5 \over 8}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction.\({9 \over 3} \ - \ {3 \over 5} = \)\( \ {9 \times 5 \ - \ 3 \times 3 \over 3\times5} = \)\({36 \over 15}\)

Then, simplify the result. \({36 \over 15} = { 12 \over 5}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({7 \over 11} \ + \ {16 \over 17} = \)\( \ {7 \times 17 \ + \ 16 \times 11 \over 11\times17} =\)\({295 \over 187}\)

**Solution**

For “

**unlike**” fractions, the first step is to find the same denominator before you can add or subtract fractions with different denominators.

To find the same denominator, Multiply two denominators, and each numerator by the denominator of the other fraction. \({8 \over 9} \ + \ {15 \over 10} = \)\( \ {8 \times 10 \ + \ 15 \times 9 \over 9\times10} = \)\({215 \over 90}\)

Then, simplify the result. \({215 \over 90} = { 43 \over 18} \)

## Add and Subtract Rational Numbers Quiz

### More Math Articles

- Understanding the Classification of Rational Numbers
- How to Simplify Fractions
- How to Add and Subtract Fractions
- How to Multiply Mixed Numbers
- How to Compare Decimals
- How to Multiply and Divide Fractions
- How to Add Mixed Numbers
- How to Round Off Decimals
- How to Subtract Mixed Numbers
- How to Divide Mixed Numbers
- How to Add or Subtract Decimals
- How to Multiply or Divide Decimals
- How to Convert between Fractions, Decimals and Mixed Numbers
- How to Factor Numbers
- How to Find the Greatest Common Factor (GCF)
- How to Find the Least Common Multiple (LCM)
- What are the Divisibility Rules