Describe how you would help your learner to add the following mixed fractions: a) 8 2/3 + 1 5/6 b) 5 2/5 + 9 3/7 c) 3 7/10 + 6 4/5

Mathematics
Describe how you would help your learner to add the following mixed fractions: a) 8 2/3 + 1 5/6 b) 5 2/5 + 9 3/7 c) 3 7/10 + 6 4/5

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Answer

3163\frac{1}{6}

Example: 123+321\frac{2}{3} + \frac{3}{2}

This shows the general method: convert mixed numbers to improper fractions, find LCD, add, and convert back to mixed. The same steps apply to a), b), and c).

Step 1: Convert mixed number to improper fraction.
123=1×3+23=531\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}
Second fraction: 32\frac{3}{2}

Step 2: Find LCD of 3 and 2: 6.
53=5×23×2=106\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
32=3×32×3=96\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}

Step 3: Add numerators.
106+96=196\frac{10}{6} + \frac{9}{6} = \frac{19}{6}

Step 4: Convert to mixed number.
19÷6=319 \div 6 = 3 remainder 1, so 3163\frac{1}{6}

Final answer: 3\frac{1{6}}

a) 523+935\frac{2}{3} + \frac{9}{3}
Using the same method (denominators match, so LCD = 3).

Step 1: Convert mixed number.
523=5×3+23=1735\frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{17}{3}
Second fraction: 93\frac{9}{3}

Step 2: LCD is 3 (no conversion needed).

Step 3: Add numerators.
173+93=263\frac{17}{3} + \frac{9}{3} = \frac{26}{3}

Step 4: Convert to mixed number.
26÷3=826 \div 3 = 8 remainder 2, so 8238\frac{2}{3}

Final answer: 8\frac{2{3}}

b) 635+956\frac{3}{5} + \frac{9}{5}
Using the same method (denominators match, so LCD = 5).

Step 1: Convert mixed number.
635=6×5+35=3356\frac{3}{5} = \frac{6 \times 5 + 3}{5} = \frac{33}{5}
Second fraction: 95\frac{9}{5}

Step 2: LCD is 5 (no conversion needed).

Step 3: Add numerators.
335+95=425\frac{33}{5} + \frac{9}{5} = \frac{42}{5}

Step 4: Convert to mixed number.
42÷5=842 \div 5 = 8 remainder 2, so 8258\frac{2}{5}

Final answer: 8\frac{2{5}}

c) 3710+6453\frac{7}{10} + 6\frac{4}{5}
Using the same method as the example (LCD needed).

Step 1: Convert both to improper fractions.
3710=3×10+710=37103\frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{37}{10}
645=6×5+45=3456\frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{34}{5}

Step 2: LCD of 10 and 5: 10.
3710\frac{37}{10} (already)
345=34×25×2=6810\frac{34}{5} = \frac{34 \times 2}{5 \times 2} = \frac{68}{10}

Step 3: Add numerators.
3710+6810=10510\frac{37}{10} + \frac{68}{10} = \frac{105}{10}

Step 4: Convert to mixed number (or simplify first).
10510=212\frac{105}{10} = \frac{21}{2}
21÷2=1021 \div 2 = 10 remainder 1, so 101210\frac{1}{2}

Final answer: 10\frac{1{2}}

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Quick Answer

Example: 1(2)/(3) + (3)/(2) This shows the general method: convert mixed numbers to improper fractions, find LCD, add, and convert back to mixed.

Describe how you would help your learner to add the following mixed fractions: a) 8 2/3 + 1 5/6 b) 5 2/5 + 9 3/7 c) 3 7/10 + 6 4/5
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Example: 1(2)/(3) + (3)/(2) This shows the general method: convert mixed numbers to improper fractions, find LCD, add, and convert back to mixed. The same steps apply to a), b), and c). Step 1: Convert mixed number to improper fraction. 1(2)/(3) = (1 × 3 + 2)/(3) = (5)/(3) Second fraction: (3)/(2) Step 2: Find LCD of 3 and 2: 6. (5)/(3) = (5 × 2)/(3 × 2) = (10)/(6) (3)/(2) = (3 × 3)/(2 × 3) = (9)/(6) Step 3: Add numerators. (10)/(6) + (9)/(6) = (19)/(6) Step 4: Convert to mixed number. 19 ÷ 6 = 3 remainder 1, so 3(1)/(6) Final answer: 3(1)/(6) a) 5(2)/(3) + (9)/(3) Using the same method (denominators match, so LCD = 3). Step 1: Convert mixed number. 5(2)/(3) = (5 × 3 + 2)/(3) = (17)/(3) Second fraction: (9)/(3) Step 2: LCD is 3 (no conversion needed). Step 3: Add numerators. (17)/(3) + (9)/(3) = (26)/(3) Step 4: Convert to mixed number. 26 ÷ 3 = 8 remainder 2, so 8(2)/(3) Final answer: 8(2)/(3) b) 6(3)/(5) + (9)/(5) Using the same method (denominators match, so LCD = 5). Step 1: Convert mixed number. 6(3)/(5) = (6 × 5 + 3)/(5) = (33)/(5) Second fraction: (9)/(5) Step 2: LCD is 5 (no conversion needed). Step 3: Add numerators. (33)/(5) + (9)/(5) = (42)/(5) Step 4: Convert to mixed number. 42 ÷ 5 = 8 remainder 2, so 8(2)/(5) Final answer: 8(2)/(5) c) 3(7)/(10) + 6(4)/(5) Using the same method as the example (LCD needed). Step 1: Convert both to improper fractions. 3(7)/(10) = (3 × 10 + 7)/(10) = (37)/(10) 6(4)/(5) = (6 × 5 + 4)/(5) = (34)/(5) Step 2: LCD of 10 and 5: 10. (37)/(10) (already) (34)/(5) = (34 × 2)/(5 × 2) = (68)/(10) Step 3: Add numerators. (37)/(10) + (68)/(10) = (105)/(10) Step 4: Convert to mixed number (or simplify first). (105)/(10) = (21)/(2) 21 ÷ 2 = 10 remainder 1, so 10(1)/(2) Final answer: 10(1)/(2)