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

ScanSolve AI Answer

Answer

517305\frac{17}{30}

a) 325+2163\frac{2}{5} + 2\frac{1}{6}

Step 1: Add the whole numbers.
3+2=53 + 2 = 5

Step 2: Add the fractions 25+16\frac{2}{5} + \frac{1}{6}.
Find the least common multiple (LCM) of 5 and 6: LCM = 30.

25=2×65×6=1230\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
16=1×56×5=530\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
1230+530=1730\frac{12}{30} + \frac{5}{30} = \frac{17}{30}

Step 3: Combine the results.
Since 1730<1\frac{17}{30} < 1, the sum is 517305\frac{17}{30}.

5\frac{17{30}}

b) 634+9236\frac{3}{4} + 9\frac{2}{3}

Step 1: Add the whole numbers.
6+9=156 + 9 = 15

Step 2: Add the fractions 34+23\frac{3}{4} + \frac{2}{3}.
Find the LCM of 4 and 3: LCM = 12.

34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
912+812=1712\frac{9}{12} + \frac{8}{12} = \frac{17}{12}

Step 3: Convert 1712\frac{17}{12} to a mixed number.
17÷12=117 \div 12 = 1 remainder 55, since 12×1=1212 \times 1 = 12 and 17−12=517 - 12 = 5.
So, 1712=1512\frac{17}{12} = 1\frac{5}{12}.

Step 4: Combine the results.
15+1512=1651215 + 1\frac{5}{12} = 16\frac{5}{12}.

16\frac{5{12}}

c) 3710+6543\frac{7}{10} + 6\frac{5}{4}

Step 1: Add the whole numbers.
3+6=93 + 6 = 9

Step 2: Add the fractions 710+54\frac{7}{10} + \frac{5}{4}.
Find the LCM of 10 and 4: LCM = 20.

710=7×210×2=1420\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20}
54=5×54×5=2520\frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20}
1420+2520=3920\frac{14}{20} + \frac{25}{20} = \frac{39}{20}

Step 3: Convert 3920\frac{39}{20} to a mixed number.
39÷20=139 \div 20 = 1 remainder 1919, since 20×1=2020 \times 1 = 20 and 39−20=1939 - 20 = 19.
So, 3920=11920\frac{39}{20} = 1\frac{19}{20}.

Step 4: Combine the results.
9+11920=1019209 + 1\frac{19}{20} = 10\frac{19}{20}.

10\frac{19{20}}

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.

More Mathematics Questions

QKando limited received an invoice from a supplier for K28500. The terms of payment offered were a 5%…QGive me paper one of mathematics kcse 2024 section A questions and answersQPlease Draw Using a ruler and a pair of compases Only construct the following angles 5° 135°QJournal riyazi TCS School maliya malayatti riyasi chapter ka naam hai aur is chapter mein 4.1 exerci…QQUESTION 2 John decided to start a car wash service on Saturdays in his matric year. He rented a Pow…
See all Mathematics questions →

Still have questions?

Quick Answer

a) 3(2)/(5) + 2(1)/(6) Step 1: Add the whole numbers. 3 + 2 = 5 Step 2: Add the fractions (2)/(5) + (1)/(6).

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
a) 3(2)/(5) + 2(1)/(6) Step 1: Add the whole numbers. 3 + 2 = 5 Step 2: Add the fractions (2)/(5) + (1)/(6). Find the least common multiple (LCM) of 5 and 6: LCM = 30. (2)/(5) = (2 × 6)/(5 × 6) = (12)/(30) (1)/(6) = (1 × 5)/(6 × 5) = (5)/(30) (12)/(30) + (5)/(30) = (17)/(30) Step 3: Combine the results. Since (17)/(30) < 1, the sum is 5(17)/(30). 5(17)/(30) b) 6(3)/(4) + 9(2)/(3) Step 1: Add the whole numbers. 6 + 9 = 15 Step 2: Add the fractions (3)/(4) + (2)/(3). Find the LCM of 4 and 3: LCM = 12. (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) (9)/(12) + (8)/(12) = (17)/(12) Step 3: Convert (17)/(12) to a mixed number. 17 ÷ 12 = 1 remainder 5, since 12 × 1 = 12 and 17 - 12 = 5. So, (17)/(12) = 1(5)/(12). Step 4: Combine the results. 15 + 1(5)/(12) = 16(5)/(12). 16(5)/(12) c) 3(7)/(10) + 6(5)/(4) Step 1: Add the whole numbers. 3 + 6 = 9 Step 2: Add the fractions (7)/(10) + (5)/(4). Find the LCM of 10 and 4: LCM = 20. (7)/(10) = (7 × 2)/(10 × 2) = (14)/(20) (5)/(4) = (5 × 5)/(4 × 5) = (25)/(20) (14)/(20) + (25)/(20) = (39)/(20) Step 3: Convert (39)/(20) to a mixed number. 39 ÷ 20 = 1 remainder 19, since 20 × 1 = 20 and 39 - 20 = 19. So, (39)/(20) = 1(19)/(20). Step 4: Combine the results. 9 + 1(19)/(20) = 10(19)/(20). 10(19)/(20)