Why integration multiplies value in Google Sheets - Formula Trace Breakdown

Sample Data

This data shows time in hours and speed in kilometers per hour for a car trip.

Cell	Value
A1	Time (hours)
B1	Speed (km/h)
A2	1
B2	60
A3	2
B3	70
A4	3
B4	80

Formula Trace

=SUMPRODUCT(B2:B3, A3:A4 - A2:A3)

Step 1: A3:A4 - A2:A3

Step 2: B2:B3

Step 3: B2:B3 * (A3:A4 - A2:A3)

Step 4: SUMPRODUCT(B2:B3, A3:A4 - A2:A3)

Cell Reference Map

    A       B
1 Time   Speed
2  1      60  
3  2      70  
4  3      80  

References:
- B2:B3 speeds for intervals
- A3:A4 and A2:A3 for time differences

The formula uses speeds from B2 to B3 and time differences between A3:A4 and A2:A3 to calculate distance.

Result

    A       B       C
1 Time   Speed   Distance
2  1      60      
3  2      70      
4  3      80      130

Cell C4 shows total distance = 130 km

The final result 130 km is the total distance traveled, calculated by multiplying speed by time intervals and adding them up.

Sheet Trace Quiz - 3 Questions

What does the expression (A3:A4 - A2:A3) calculate?

A Total time

B Time intervals between measurements

C Speed differences

D Sum of speeds

Key Result

SUMPRODUCT multiplies corresponding elements of two arrays and sums the results to calculate total accumulated value.

Practice

1. What does the SUMPRODUCT function do in Google Sheets?

easy

A. It multiplies corresponding elements in arrays and sums the results.

B. It adds all numbers in a single range without multiplication.

C. It finds the average of numbers in a range.

D. It counts the number of cells with numbers.

Solution

1. Step 1: Understand the function purpose

   SUMPRODUCT multiplies elements from two or more arrays element-wise.

2. Step 2: Sum the multiplied results

   After multiplying, it adds all those products to give a total sum.

3. Final Answer:

   It multiplies corresponding elements in arrays and sums the results. -> Option A

4. Quick Check:

   SUMPRODUCT = multiply then sum [OK]

Hint: Remember: multiply pairs, then add all products [OK]

Common Mistakes:

• Thinking SUMPRODUCT only sums without multiplying
• Confusing SUMPRODUCT with SUM or AVERAGE
• Assuming it counts cells instead of calculating products

2. Which of these is the correct syntax to multiply two ranges A1:A3 and B1:B3 and sum the results in Google Sheets?

easy

A. =A1:A3*B1:B3

B. =SUMPRODUCT(A1:A3, B1:B3)

C. =PRODUCT(SUM(A1:A3), SUM(B1:B3))

D. =SUM(A1:A3)+SUM(B1:B3)

Solution

1. Step 1: Check formula for multiplying and summing pairs

   =SUMPRODUCT(A1:A3, B1:B3) multiplies each pair and sums the results correctly.

2. Step 2: Verify other options

   =A1:A3*B1:B3 multiplies element-wise but returns an array spill instead of a single sum; =PRODUCT(SUM(A1:A3), SUM(B1:B3)) multiplies sums, not pairs; =SUM(A1:A3)+SUM(B1:B3) just adds sums.

3. Final Answer:

   =SUMPRODUCT(A1:A3, B1:B3) -> Option B

4. Quick Check:

   Correct syntax for pairwise multiply and sum is SUMPRODUCT [OK]

Hint: Use SUMPRODUCT for pairwise multiply and sum [OK]

Common Mistakes:

• Using * directly between ranges without SUM (array spill)
• Multiplying sums instead of element-wise pairs
• Adding sums instead of multiplying pairs

3. Given columns:
A1:A3 = {2, 3, 4}
B1:B3 = {5, 6, 7}
What is the result of =SUMPRODUCT(A1:A3, B1:B3)?

medium

A. 56

B. 72

C. 54

D. 90

Solution

1. Step 1: Multiply each pair of elements

   2*5=10, 3*6=18, 4*7=28

2. Step 2: Sum all products

   10 + 18 + 28 = 56

3. Final Answer:

   56 -> Option A

4. Quick Check:

   Sum of products = 56 [OK]

Hint: Multiply pairs, then add all results [OK]

Common Mistakes:

• Adding elements instead of multiplying
• Multiplying sums instead of element-wise
• Miscalculating individual products

4. You wrote =SUMPRODUCT(A1:A3, B1:B2) but get an error. What is the problem?

medium

A. You need to use SUM instead of SUMPRODUCT.

B. SUMPRODUCT cannot multiply ranges with numbers.

C. Ranges have different lengths, causing mismatch error.

D. Formula is missing parentheses.

Solution

1. Step 1: Check range sizes

   A1:A3 has 3 cells, B1:B2 has 2 cells; lengths differ.

2. Step 2: Understand SUMPRODUCT requirement

   SUMPRODUCT requires ranges to be same size to multiply pairs element-wise.

3. Final Answer:

   Ranges have different lengths, causing mismatch error. -> Option C

4. Quick Check:

   SUMPRODUCT needs equal-length ranges [OK]

Hint: Ensure ranges have same number of cells [OK]

Common Mistakes:

• Ignoring range size mismatch
• Thinking SUMPRODUCT works with different sized ranges
• Assuming syntax error instead of range mismatch

5. You have hourly rates in A1:A4 = {10, 15, 20, 25} and hours worked in B1:B4 = {2, 3, 1, 4}. Which formula calculates total earnings correctly?

hard

A. =SUM(A1:A4)*SUM(B1:B4)

B. =PRODUCT(A1:A4, B1:B4)

C. =SUM(A1:A4+B1:B4)

D. =SUMPRODUCT(A1:A4, B1:B4)

Solution

1. Step 1: Understand what total earnings mean

   Total earnings = sum of (rate * hours) for each entry.

2. Step 2: Choose formula that multiplies pairs and sums

   =SUMPRODUCT(A1:A4, B1:B4) multiplies each rate by hours and sums all.

3. Final Answer:

   =SUMPRODUCT(A1:A4, B1:B4) -> Option D

4. Quick Check:

   Use SUMPRODUCT for total of multiplied pairs [OK]

Hint: Multiply pairs then sum with SUMPRODUCT [OK]

Common Mistakes:

• Multiplying sums instead of pairs
• Adding rates and hours directly
• Using PRODUCT which multiplies all cells together