Complete the Equation: How to Finish Subtraction and Addition Sentences with Mixed Numbers
Mixed numbers, which combine whole numbers and fractions, are frequently encountered in various mathematical and real-world contexts.
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When presented with incomplete addition or subtraction sentences involving mixed numbers, the challenge lies in determining the missing value. In this guide, we’ll explore how to finish such sentences, ensuring a clear understanding of the operations involved.
Step-by-step Guide to Complete the Equation:
1. Understanding the Sentence Structure:
Incomplete sentences will typically have a missing value, represented by a blank or a variable (like \(x\)). Your task is to determine this missing value.
2. Approaching Addition Sentences:
For addition:
– Begin by adding/subtracting the fractional parts. If the fractions have different denominators, find a common denominator.
– Next, add/subtract the whole numbers.
– Combine the results to get the final mixed number.
3. Approaching Subtraction Sentences:
For subtraction:
– Start by subtracting the fractional parts. If the fraction from which you are subtracting is larger than the first fraction, borrow from the whole number.
– Then, subtract the whole numbers.
– Combine the results to get the final mixed number.
Example 1 (Addition):
Complete the sentence: \( 2 \frac{1}{4} + 3 \frac{3}{4} = \_\_\_\_ \)
Solution:
Adding the fractions: \(\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1\)
Adding the whole numbers: \(2 + 3 + 1 (from the fractions) = 6\)
The completed sentence is: \( 2 \frac{1}{4} + 3 \frac{3}{4} = 6 \)
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Example 2 (Subtraction):
Complete the sentence: \( 5 \frac{3}{5} – 2 \frac{2}{5} = \_\_\_\_ \)
Solution:
Subtracting the fractions: \(\frac{3}{5} – \frac{2}{5} = \frac{1}{5}\)
Subtracting the whole numbers: \(5 – 2 = 3\)
The completed sentence is: \( 5 \frac{3}{5} – 2 \frac{2}{5} = 3 \frac{1}{5} \)
Practice Questions:
1. Complete the sentence: \( 4 \frac{2}{7} + 3 \frac{5}{7} = \_\_\_\_ \)
2. Complete the sentence: \( 7 \frac{3}{8} – 5 \frac{1}{8} = \_\_\_\_ \)
3. Complete the sentence: \( 6 \frac{1}{6} + 2 \frac{5}{6} = \_\_\_\_ \)
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Answers:
1. \( 8 \)
2. \( 2 \frac{2}{8} \) or \( 2 \frac{1}{4} \)
3. \( 9 \)
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