Add the following: 1) 2 3/8 + 1 1/8; 2) 7 1/5 + 3 2/5. Multiply the following: 3) 2 x 1 1/8; 4) 3 x 3 1/5

Mathematics
Add the following: 1) 2 3/8 + 1 1/8; 2) 7 1/5 + 3 2/5. Multiply the following: 3) 2 x 1 1/8; 4) 3 x 3 1/5

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Answer

\dfrac{29}{24}

Add 12+38+13\frac{1}{2} + \frac{3}{8} + \frac{1}{3}.

Step 1: Find LCD of denominators 2, 8, 3.
LCD=23×3=24LCD = 2^3 \times 3 = 24

Step 2: Convert 12\frac{1}{2}.
12=1×122×12=1224\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}

Step 3: Convert 38\frac{3}{8}.
38=3×38×3=924\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}

Step 4: Convert 13\frac{1}{3}.
13=1×83×8=824\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}

Step 5: Add the fractions.
1224+924+824=12+9+824=2924\frac{12}{24} + \frac{9}{24} + \frac{8}{24} = \frac{12 + 9 + 8}{24} = \frac{29}{24}

Step 6: 2924\frac{29}{24} is in simplest form (29 is prime).
Final answer: 2924\boxed{\dfrac{29}{24}}

Add 75+32\frac{7}{5} + \frac{3}{2}.

Step 1: Find LCD of denominators 5, 2.
LCD=5×2=10LCD = 5 \times 2 = 10

Step 2: Convert 75\frac{7}{5}.
75=7×25×2=1410\frac{7}{5} = \frac{7 \times 2}{5 \times 2} = \frac{14}{10}

Step 3: Convert 32\frac{3}{2}.
32=3×52×5=1510\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}

Step 4: Add the fractions.
1410+1510=14+1510=2910\frac{14}{10} + \frac{15}{10} = \frac{14 + 15}{10} = \frac{29}{10}

Step 5: 2910\frac{29}{10} is in simplest form.
Final answer: 2910\boxed{\dfrac{29}{10}}

Multiply 22×15\frac{2}{2} \times \frac{1}{5}.

Step 1: Multiply numerators and denominators.
22×15=2×12×5=210\frac{2}{2} \times \frac{1}{5} = \frac{2 \times 1}{2 \times 5} = \frac{2}{10}

Step 2: Simplify 210\frac{2}{10}.
2÷210÷2=15\frac{2 \div 2}{10 \div 2} = \frac{1}{5}

Final answer: 15\boxed{\dfrac{1}{5}}

Multiply 3×353 \times \frac{3}{5}.

Step 1: Write 3 as 31\frac{3}{1}.
3×35=31×353 \times \frac{3}{5} = \frac{3}{1} \times \frac{3}{5}

Step 2: Multiply numerators and denominators.
3×31×5=95\frac{3 \times 3}{1 \times 5} = \frac{9}{5}

Step 3: 95\frac{9}{5} is in simplest form.
Final answer: 95\boxed{\dfrac{9}{5}}

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Problem 1 Add (1)/(2) + (3)/(8) + (1)/(3). Step 1: Find LCD of denominators 2, 8, 3.

Add the following: 1) 2 3/8 + 1 1/8; 2) 7 1/5 + 3 2/5. Multiply the following: 3) 2 x 1 1/8; 4) 3 x 3 1/5
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
Problem 1 Add (1)/(2) + (3)/(8) + (1)/(3). Step 1: Find LCD of denominators 2, 8, 3. LCD = 2^3 × 3 = 24 Step 2: Convert (1)/(2). (1)/(2) = (1 × 12)/(2 × 12) = (12)/(24) Step 3: Convert (3)/(8). (3)/(8) = (3 × 3)/(8 × 3) = (9)/(24) Step 4: Convert (1)/(3). (1)/(3) = (1 × 8)/(3 × 8) = (8)/(24) Step 5: Add the fractions. (12)/(24) + (9)/(24) + (8)/(24) = (12 + 9 + 8)/(24) = (29)/(24) Step 6: (29)/(24) is in simplest form (29 is prime). Final answer: (29)/(24) Problem 2 Add (7)/(5) + (3)/(2). Step 1: Find LCD of denominators 5, 2. LCD = 5 × 2 = 10 Step 2: Convert (7)/(5). (7)/(5) = (7 × 2)/(5 × 2) = (14)/(10) Step 3: Convert (3)/(2). (3)/(2) = (3 × 5)/(2 × 5) = (15)/(10) Step 4: Add the fractions. (14)/(10) + (15)/(10) = (14 + 15)/(10) = (29)/(10) Step 5: (29)/(10) is in simplest form. Final answer: (29)/(10) Problem 3 Multiply (2)/(2) × (1)/(5). Step 1: Multiply numerators and denominators. (2)/(2) × (1)/(5) = (2 × 1)/(2 × 5) = (2)/(10) Step 2: Simplify (2)/(10). (2 ÷ 2)/(10 ÷ 2) = (1)/(5) Final answer: (1)/(5) Problem 4 Multiply 3 × (3)/(5). Step 1: Write 3 as (3)/(1). 3 × (3)/(5) = (3)/(1) × (3)/(5) Step 2: Multiply numerators and denominators. (3 × 3)/(1 × 5) = (9)/(5) Step 3: (9)/(5) is in simplest form. Final answer: (9)/(5)