Math Problem Statement

What do you add to 13/4 to make 4? How much do you need to subtract from 29/6 to make 4? How much do you need to subtract from 77/10 to make 7? What do you add to 2 3/8 to make 6? What do you add to 2 3/7 to make 4? What do you add to 2 8/9 to make 5?

Solution

Let’s go through each of the questions shown in the image and solve them one by one.

Question 1:

What do you add to 134\frac{13}{4} to make 4?

We can convert 4 into a fraction with the same denominator: 4=1644 = \frac{16}{4} Now, subtract 134\frac{13}{4} from 164\frac{16}{4}: 164134=16134=34\frac{16}{4} - \frac{13}{4} = \frac{16 - 13}{4} = \frac{3}{4} So, you need to add 34\frac{3}{4}.

Question 2:

How much do you need to subtract from 296\frac{29}{6} to make 4?

Convert 4 into a fraction with denominator 6: 4=2464 = \frac{24}{6} Now subtract 246\frac{24}{6} from 296\frac{29}{6}: 296246=29246=56\frac{29}{6} - \frac{24}{6} = \frac{29 - 24}{6} = \frac{5}{6} So, you need to subtract 56\frac{5}{6}.

Question 3:

How much do you need to subtract from 7710\frac{77}{10} to make 7?

Convert 7 into a fraction with denominator 10: 7=70107 = \frac{70}{10} Now subtract 7010\frac{70}{10} from 7710\frac{77}{10}: 77107010=777010=710\frac{77}{10} - \frac{70}{10} = \frac{77 - 70}{10} = \frac{7}{10} So, you need to subtract 710\frac{7}{10}.

Question 4:

What do you add to 2382 \frac{3}{8} to make 6?

First, convert 2382 \frac{3}{8} into an improper fraction: 238=1982 \frac{3}{8} = \frac{19}{8} Now convert 6 into a fraction with denominator 8: 6=4886 = \frac{48}{8} Subtract 198\frac{19}{8} from 488\frac{48}{8}: 488198=48198=298\frac{48}{8} - \frac{19}{8} = \frac{48 - 19}{8} = \frac{29}{8} So, you need to add 298\frac{29}{8}.

Question 5:

What do you add to 2372 \frac{3}{7} to make 4?

First, convert 2372 \frac{3}{7} into an improper fraction: 237=1772 \frac{3}{7} = \frac{17}{7} Now convert 4 into a fraction with denominator 7: 4=2874 = \frac{28}{7} Subtract 177\frac{17}{7} from 287\frac{28}{7}: 287177=28177=117\frac{28}{7} - \frac{17}{7} = \frac{28 - 17}{7} = \frac{11}{7} So, you need to add 117\frac{11}{7}.

Question 6:

What do you add to 2892 \frac{8}{9} to make 5?

First, convert 2892 \frac{8}{9} into an improper fraction: 289=2692 \frac{8}{9} = \frac{26}{9} Now convert 5 into a fraction with denominator 9: 5=4595 = \frac{45}{9} Subtract 269\frac{26}{9} from 459\frac{45}{9}: 459269=45269=199\frac{45}{9} - \frac{26}{9} = \frac{45 - 26}{9} = \frac{19}{9} So, you need to add 199\frac{19}{9}.


Would you like further clarification on any of the steps?

Here are some additional related questions:

  1. How can you convert mixed numbers to improper fractions and vice versa?
  2. What strategies can you use to find a common denominator between two fractions?
  3. How do you simplify fractions after performing addition or subtraction?
  4. What is the difference between proper and improper fractions?
  5. How can you subtract mixed numbers without converting them to improper fractions?

Tip: When adding or subtracting mixed numbers, it is often easier to convert them into improper fractions first!

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Math Problem Analysis

Mathematical Concepts

Fractions
Addition
Subtraction
Mixed Numbers

Formulas

Addition of fractions: a/b + c/b = (a+c)/b
Subtraction of fractions: a/b - c/b = (a-c)/b
Converting mixed numbers to improper fractions

Theorems

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Suitable Grade Level

Grades 6-8