Sensim Math Original · sm-1
Easy mode Grade 5Problem
Imagine a baker writing down how many kilograms of flour go into one big batch of bread. Instead of one tidy number, the baker wrote the total as three fractions added together.
Here is the sum the baker wrote:
Work out the total. Write your answer as a decimal.
Pick an answer.
Toolkit + CCSS Solution
Understand
Restated: A baker has written the total flour for a big batch as $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$ (in kilograms). We need to find this value as a decimal and match it to one of the five answer choices.
Givens: A sum of three fractions: $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$; Each fraction has a clean common factor (9, 15, and 7 respectively), so each term reduces to a simple decimal; Five answer choices: (A) 10.09, (B) 10.509, (C) 10.59, (D) 10.9, (E) 10.95
Unknowns: The decimal value of the entire sum
Understand
Restated: A baker has written the total flour for a big batch as $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$ (in kilograms). We need to find this value as a decimal and match it to one of the five answer choices.
Givens: A sum of three fractions: $\frac{72}{9} + \frac{75}{30} + \frac{63}{700}$; Each fraction has a clean common factor (9, 15, and 7 respectively), so each term reduces to a simple decimal; Five answer choices: (A) 10.09, (B) 10.509, (C) 10.59, (D) 10.9, (E) 10.95
Plan
Primary tool: #7 Identify Subproblems
Secondary: #3 Eliminate Possibilities
Trying to add the three fractions with a common denominator at once (e.g. $6300$) gives messy multi-digit arithmetic. Instead we **split the sum into three independent subproblems** (Tool #7): convert each fraction to a decimal on its own, then add. Every sub-piece is small enough for mental arithmetic. Since the problem is multiple-choice, we close with **Tool #3 (Eliminate Possibilities)** to confirm our value against the five offered decimals.
Execute — Answer: C
3.OA.C.7 Step 1 - Handle the first term $\frac{72}{9}$.
- Because $72 = 9 \times 8$, the division comes out exactly and the fraction equals the whole number $8$.
💡 Fluency with multiplication and division within 100 is a Grade 3 standard, so $72 \div 9$ is immediate.
4.NF.A.1 Step 2 - Handle the second term $\frac{75}{30}$.
- Dividing numerator and denominator both by $15$ gives the equivalent fraction $\frac{5}{2}$.
- (You can also do it in two steps: divide by $5$ to get $\frac{15}{6}$, then by $3$ to reach $\frac{5}{2}$.)
💡 Dividing the numerator and denominator by a common factor to get an equivalent fraction is taught in Grade 4.
5.NF.B.3 Step 3 - Convert the simplified $\frac{5}{2}$ to a decimal.
- A fraction means "numerator divided by denominator," so $5 \div 2 = 2.5$.
💡 Interpreting a fraction as numerator-divided-by-denominator and writing it as a decimal is the heart of Grade 5 fractions.
4.NF.C.6 Step 4 - Handle the third term $\frac{63}{700}$.
- Dividing top and bottom by $7$ gives $\frac{9}{100}$.
- A fraction with denominator $100$ translates directly into two decimal places, so the value is $0.09$.
💡 Rewriting a fraction with denominator $10$ or $100$ in decimal notation is exactly the Grade 4 fraction-to-decimal standard.
5.NBT.B.7 Step 5 - Finally, add the three decimals, lining up the decimal points.
- The ones column gives $8+2=10$ (with a carry), the tenths column gives $0+5+0=5$, and the hundredths column gives $0+0+9=9$, so the sum is $10.59$.
💡 Adding decimals to hundredths is a Grade 5 standard; once the place values are aligned it behaves just like whole-number addition.
5.NBT.A.3 Step 6 - Cross-check against the answer choices.
- The candidates are $10.09$, $10.509$, $10.59$, $10.9$, and $10.95$.
- Our computed value $10.59$ matches choice **(C)** exactly.
- (A) $10.09$ drops the $2.5$ tenths from the second term; (B) $10.509$ has a thousandths digit our calculation never produces; (D) $10.9$ ignores the small $0.09$ piece; (E) $10.95$ has the tenths and hundredths digits swapped.
💡 Reading and comparing decimals to thousandths place-by-place is the Grade 5 standard that makes the elimination safe.
3.OA.C.7 Handle the first term $\frac{72}{9}$. Because $72 = 9 \times 8$, the division co 4.NF.A.1 Handle the second term $\frac{75}{30}$. Dividing numerator and denominator both 5.NF.B.3 Convert the simplified $\frac{5}{2}$ to a decimal. A fraction means "numerator d 4.NF.C.6 Handle the third term $\frac{63}{700}$. Dividing top and bottom by $7$ gives $\f 5.NBT.B.7 Finally, add the three decimals, lining up the decimal points. The ones column g 5.NBT.A.3 Cross-check against the answer choices. The candidates are $10.09$, $10.509$, $1 Review
Reasonableness: Quick magnitude check: the first term is $8$, the second is between $2$ and $3$, and the third is a tiny number close to $0$, so the sum should land near $8 + 2.5 + 0 \approx 10.5$. The value $10.59$ sits exactly where we expect, with the small extra $0.09$ from the third term accounted for. Choices like $10.9$ ignore the hundredths digit, $10.95$ has the digits flipped, $10.09$ throws away the $2.5$ entirely, and $10.509$ has a thousandths digit that our calculation cannot produce.
Alternative: An alternative is Tool #13 (Convert to Algebra): give all three fractions a common denominator of $6300$, add the numerators, then convert. $\frac{50400}{6300} + \frac{15750}{6300} + \frac{567}{6300} = \frac{66717}{6300} = 10.59$. The answer is the same, but the arithmetic is heavier, so splitting term-by-term with Tool #7 is the friendlier path for an elementary student.
CCSS standards used (min grade 5)
3.OA.C.7Fluently multiply and divide within 100 (Computing $72 \div 9 = 8$ in one step.)4.NF.A.1Explain why a fraction is equivalent to another fraction (Reducing $\frac{75}{30}$ to the equivalent fraction $\frac{5}{2}$ by dividing numerator and denominator by $15$.)4.NF.C.6Use decimal notation for fractions with denominators 10 or 100 (Rewriting $\frac{9}{100}$ as the decimal $0.09$.)5.NF.B.3Interpret a fraction as division of the numerator by the denominator (Converting $\frac{5}{2}$ to the decimal $2.5$ via $5 \div 2$.)5.NBT.A.3Read, write, and compare decimals to thousandths (Comparing the computed value to the five decimal answer choices $10.09$, $10.509$, $10.59$, $10.9$, $10.95$ digit by digit.)5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths (Performing the final aligned-decimal addition $8 + 2.5 + 0.09 = 10.59$.)
⭐ This problem only needs Grade 5 fraction-to-decimal conversion and decimal addition you already know!
⭐ This problem only needs Grade 5 fraction-to-decimal conversion and decimal addition you already know!