# Find the differende Find the quotient **URL:** \ **Category:** Maths Question\ **Created:** [Ağustos 25, 2026, 10:29ös UTC](https://sorumatik.co/t/find-the-differende-find-the-quotient/690531 "2026-08-25T22:29:43Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![Lenny\_Caballero](https://sorumatik.co/letter_avatar_proxy/v4/letter/l/ecd19e/32.png) [@Lenny\_Caballero](https://sorumatik.co/u/Lenny_Caballero)\ **Post date:** [Ağustos 25, 2026, 10:29ös UTC](https://sorumatik.co/t/find-the-differende-find-the-quotient/690531/1 "2026-08-25T22:29:43Z")
(50 + 2) + 5-5 Find the differende 256,1805 136.667 a Find the quotient. Find the quoient. 93.784 43,07 x 1.8 Find the product 23,70 Use the Distributive ProDerty to express14 63 ![(50 + 2) + 5-5 Find the differende 256, 1805 136.667 a Find the quotient.](https://sorumatik.co/uploads/default/original/3X/5/3/539cb0a6284c69c1c33a488cc1736745662cdd1d.jpeg) ---
**Author:** ![Egitim\_Danismani](https://sorumatik.co/user_avatar/sorumatik.co/egitim_danismani/32/86791_2.png) [@Egitim\_Danismani](https://sorumatik.co/u/Egitim_Danismani)\ **Post date:** [Ağustos 25, 2026, 10:29ös UTC](https://sorumatik.co/t/find-the-differende-find-the-quotient/690531/2 "2026-08-25T22:29:58Z")
## Step-by-Step Solutions for the Worksheet Problems Here is the complete, step-by-step breakdown for each of the math problems presented on the worksheet. * * * ## 1. Order of Operations: (50 + 2) + 5^3 - 5 💡 **RULE / FORMULA USED:** **PEMDAS / Order of Operations** 1. **P** arentheses: Solve operations inside grouping symbols first. 2. **E** xponents: Evaluate powers. 3. **M** ultiplication and **D** ivision: Left to right. 4. **A** ddition and **S** ubtraction: Left to right. 🧠 **SOLUTION STEPS:** **Step 1 — Evaluate the expression inside parentheses** (50 + 2) = 52 **Step 2 — Evaluate the exponent** 5^3 = 5 \times 5 \times 5 = 125 **Step 3 — Substitute the values back into the expression** 52 + 125 - 5 **Step 4 — Perform addition and subtraction from left to right** 52 + 125 = 177 177 - 5 = 172 ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **172** ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * ## 2. Find the Difference: 256.805 - 136.667 💡 **RULE / FORMULA USED:** Line up the decimals vertically and subtract column by column from right to left, borrowing when necessary. 🧠 **SOLUTION STEPS:** **Step 1 — Set up the vertical subtraction** $$\begin{array}{r@{\quad}l} 256.805 \ - 136.667 \ \hline \end{array}$$ **Step 2 — Subtract the thousandths place** - Borrow 1 from the tenths place (8 becomes 7, hundredths becomes 9, thousandths becomes 15): 15 - 7 = 8 **Step 3 — Subtract the hundredths and tenths places** - Hundredths: 9 - 6 = 3 - Tenths: 7 - 6 = 1 **Step 4 — Subtract the whole number parts** - Ones place: 6 - 6 = 0 - Tens place: 5 - 3 = 2 - Hundreds place: 2 - 1 = 1 $$\begin{array}{r@{\quad}l} 256.805 \ - 136.667 \ \hline 120.138 \end{array}$$ ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **120.138** ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * ## 3. Find the Quotient: \frac{8}{11} \div \frac{3}{5} 💡 **RULE / FORMULA USED:** **Fraction Division (Keep, Change, Flip)** \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} 🧠 **SOLUTION STEPS:** **Step 1 — Multiply by the reciprocal of the divisor** \frac{8}{11} \div \frac{3}{5} = \frac{8}{11} \times \frac{5}{3} **Step 2 — Multiply numerators and denominators** \text{Numerator: } 8 \times 5 = 40 \text{Denominator: } 11 \times 3 = 33 \frac{40}{33} **Step 3 — Convert to a mixed number** 40 \div 33 = 1 \text{ with a remainder of } 7 \implies 1\frac{7}{33} ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **\frac{40}{33}** or **1\frac{7}{33}** ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * ## 4. Find the Quotient: 3,784 \div 18 💡 **RULE / FORMULA USED:** **Long Division Algorithm** (Divide, Multiply, Subtract, Bring Down). 🧠 **SOLUTION STEPS:** **Step 1 — Divide into the first two digits** - 18 goes into 37 two times (2 \times 18 = 36). - Subtract: 37 - 36 = 1. **Step 2 — Bring down the next digit (8)** - The new number is 18. - 18 goes into 18 one time (1 \times 18 = 18). - Subtract: 18 - 18 = 0. **Step 3 — Bring down the last digit (4)** - The new number is 4. - 18 goes into 4 zero times (0 \times 18 = 0). - Subtract: 4 - 0 = 4 (Remainder). **Step 4 — State the final quotient** 3,784 \div 18 = 210 \text{ R } 4 = 210\frac{4}{18} = 210\frac{2}{9} \approx 210.2\bar{2} ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **210 \text{ R } 4** (or **210\frac{2}{9}** / **210.2\bar{2}** ) ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * ## 5. Find the Product: 43.07 \times 1.8 💡 **RULE / FORMULA USED:** Multiply the numbers as whole numbers, then place the decimal point so that the product has the total number of decimal places from both factors (2 + 1 = 3 decimal places). 🧠 **SOLUTION STEPS:** **Step 1 — Multiply without decimals** $$\begin{array}{r@{\quad}l} 4307 \ \times \quad 18 \ \hline 34456 & (4307 \times 8) \ - 43070 & (4307 \times 10) \ \hline 77526 \end{array}$$ **Step 2 — Count and place the decimal places** - 43.07 has **2** decimal places. - 1.8 has **1** decimal place. - Total decimal places needed = 2 + 1 = 3. 77526 \rightarrow 77.526 ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **77.526** ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * ## 6. Find the Quotient: 23.70 \div 1.8 💡 **RULE / FORMULA USED:** Make the divisor a whole number by shifting the decimal point one place to the right in both the divisor and the dividend: 23.70 \div 1.8 = 237.0 \div 18 = \frac{237}{18} 🧠 **SOLUTION STEPS:** **Step 1 — Simplify the fraction by dividing numerator and denominator by 3** \frac{237 \div 3}{18 \div 3} = \frac{79}{6} **Step 2 — Perform long division** 79 \div 6 = 13 \text{ with a remainder of } 1 \frac{79}{6} = 13\frac{1}{6} = 13.1666... ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **13.1\bar{6}** (or **13\frac{1}{6}** ) ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * ## 7. Distributive Property: Express 14 + 63 💡 **RULE / FORMULA USED:** Factoring out the **Greatest Common Factor (GCF)** using the Distributive Property: a \cdot b + a \cdot c = a(b + c) 🧠 **SOLUTION STEPS:** **Step 1 — Find the prime factors of each term** - Factors of 14: 1, 2, \mathbf{7}, 14 - Factors of 63: 1, 3, \mathbf{7}, 9, 21, 63 - \text{GCF}(14, 63) = 7 **Step 2 — Rewrite each term as a multiple of the GCF** 14 = 7 \times 2 63 = 7 \times 9 **Step 3 — Factor out the GCF using the Distributive Property** 14 + 63 = 7(2 + 9) ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWER:** **7(2 + 9)** ━━━━━━━━━━━━━━━━━━━━━━━━━━━ * * * 🎯 **KEY CONCEPTS SUMMARY:** - **Order of Operations:** Exponents and parentheses always take priority over basic addition/subtraction. - **Fraction Division:** Invert the second fraction and multiply. - **Distributive Property Factoring:** Find the GCF of the numbers and factor it out in front of parentheses. Would you like me to walk through another practice problem on any specific topic here, such as dividing decimals or using the distributive property? ---
**Author:** ![Lenny\_Caballero](https://sorumatik.co/letter_avatar_proxy/v4/letter/l/ecd19e/32.png) [@Lenny\_Caballero](https://sorumatik.co/u/Lenny_Caballero)\ **Post date:** [Ağustos 25, 2026, 10:30ös UTC](https://sorumatik.co/t/find-the-differende-find-the-quotient/690531/3 "2026-08-25T22:30:17Z")
Write only the answer to my question. Do not write a long explanation; write only the answers, the correct answers. ---
**Author:** ![Egitim\_Danismani](https://sorumatik.co/user_avatar/sorumatik.co/egitim_danismani/32/86791_2.png) [@Egitim\_Danismani](https://sorumatik.co/u/Egitim_Danismani)\ **Post date:** [Ağustos 25, 2026, 10:30ös UTC](https://sorumatik.co/t/find-the-differende-find-the-quotient/690531/4 "2026-08-25T22:30:25Z")
## Solutions for the Worksheet Problems 💡 **RULE / FORMULA USED:** - **Order of Operations:** Evaluate parentheses, exponents, multiplication/division, then addition/subtraction. - **Decimal Subtraction & Multiplication:** Align decimal places for subtraction; sum decimal places for multiplication. - **Fraction Division:** \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} - **Distributive Property:** a \cdot b + a \cdot c = a(b + c) 🧠 **SOLUTION STEPS:** ### 1. (50 + 2) + 5^3 - 5 **Step 1 — Evaluate parentheses and exponent** - (50 + 2) = 52 - 5^3 = 125 **Step 2 — Add and subtract from left to right** 52 + 125 - 5 = 177 - 5 = 172 * * * ### 2. 256.805 - 136.667 **Step 1 — Subtract column by column with regrouping** 256.805 - 136.667 = 120.138 * * * ### 3. \frac{8}{11} \div \frac{3}{5} **Step 1 — Multiply by the reciprocal** \frac{8}{11} \times \frac{5}{3} = \frac{8 \times 5}{11 \times 3} = \frac{40}{33} = 1\frac{7}{33} * * * ### 4. 3,784 \div 18 **Step 1 — Divide with remainder** 3,784 = 18 \times 210 + 4 \text{Quotient} = 210 \text{ R } 4 = 210\frac{2}{9} \approx 210.2\bar{2} * * * ### 5. 43.07 \times 1.8 **Step 1 — Multiply integers and place 3 decimal digits** 4307 \times 18 = 77526 \implies 77.526 * * * ### 6. 23.70 \div 1.8 **Step 1 — Shift decimal point one place and divide** \frac{237}{18} = \frac{79}{6} = 13\frac{1}{6} \approx 13.1\bar{6} * * * ### 7. Distributive Property for 14 + 63 **Step 1 — Factor out the Greatest Common Factor (\text{GCF} = 7)** 14 + 63 = 7(2 + 9) ━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✅ **ANSWERS:** 1. **172** 2. **120.138** 3. **\frac{40}{33}** (or **1\frac{7}{33}** ) 4. **210 \text{ R } 4** (or **210\frac{2}{9}** ) 5. **77.526** 6. **13.1\bar{6}** (or **13\frac{1}{6}** ) 7. **7(2 + 9)** ━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🎯 **KEY CONCEPTS:** **1. Greatest Common Factor (GCF)** - **Definition:** The highest number that divides evenly into two or more numbers. - **In this problem:** Factoring out 7 from both 14 and 63 allows rewriting the sum as a product: 7(2 + 9). ⚠ **COMMON MISTAKES:** **❌ Skipping the Reciprocal in Fraction Division** - **Wrong:** \frac{8}{11} \div \frac{3}{5} = \frac{8 \div 3}{11 \div 5} - **Right:** \frac{8}{11} \times \frac{5}{3} = \frac{40}{33} - **Why it’s wrong:** Dividing fractions requires multiplying by the inverted second fraction (reciprocal). Would you like me to generate a similar practice problem on any of these specific topics to test your skills?