Maximum Value Comparison: Selecting the Highest-Result Exercise

Q: Why isn't 35 × 25 the biggest since 35 is the largest number?

Great question! While 35 is the largest individual factor, multiplication depends on both numbers. When 35 is paired with 25, the product is actually smaller than 30 × 30 because the factors are more balanced in the second case.

Q: Is there a pattern to predict which will be larger without calculating?

Yes! When the sum of factors is the same (like 30+30=60, 32+28=60), the pair closest to being equal gives the largest product. But when sums differ, you must calculate to be sure.

Q: What's the fastest way to multiply these numbers?

For numbers ending in 0 or 5, use shortcuts: $ 30 \times 30 = 3 \times 3 \times 100 = 900 $ and $ 35 \times 25 = 35 \times \frac{100}{4} = \frac{3500}{4} = 875 $

Q: How do I avoid calculation errors with larger numbers?

Break down the multiplication: For 32 × 28, use $ (30+2) \times (30-2) = 30^2 - 2^2 = 900 - 4 = 896 $ or use the standard algorithm step by step.

Q: Why do some factor pairs give such similar results?

Notice that 30×30, 32×28, and 33×27 all have factors that sum to 60! When factor sums are close, products tend to be close too. The more balanced the factors, the larger the product.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the largest result

00:07 We will use long multiplication for calculation

00:11 0 multiplied by any number always equals 0

00:33 This is the calculation for the first option

00:38 Let's move to the second option

00:42 We will use long multiplication for calculation

01:23 This is the calculation for the second option

01:28 Let's move to the third option

01:32 We will use long multiplication for calculation

02:06 This is the calculation for the third option

02:15 Let's move to the fourth option

02:19 We will use long multiplication for calculation

02:44 This is the calculation for the fourth option

02:56 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Choose the exercise for the highest result

2

Step-by-step solution

To solve the problem of finding the highest result from these multiplication exercises, we proceed with the following steps:

Step 1: Multiply $30 \times 30$ .
Step 2: Multiply $35 \times 25$ .
Step 3: Multiply $32 \times 28$ .
Step 4: Multiply $33 \times 27$ .
Step 5: Compare the results to find the highest product.

Let's calculate each step:

Step 1: $30 \times 30 = 900$ .

Step 2: $35 \times 25 = 875$ .

Step 3: $32 \times 28 = 896$ .

Step 4: $33 \times 27 = 891$ .

Now, compare the products:

$30 \times 30$ yields $900$ .
$35 \times 25$ yields $875$ .
$32 \times 28$ yields $896$ .
$33 \times 27$ yields $891$ .

The largest product is $900$ , which is from the calculation $30 \times 30$ .

Therefore, the option producing the highest result is $30 \times 30$ .

3

Final Answer

$30\times30$

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate each product completely before comparing values
Technique: Use standard multiplication: 30 × 30 = 900
Check: Verify all calculations and compare: 900 > 896 > 891 > 875 ✓

Common Mistakes

Avoid these frequent errors

Assuming larger individual factors give larger products
Don't think 35 × 25 is biggest because 35 is the largest single factor = wrong conclusion! The product depends on both factors together. Always calculate each multiplication completely before comparing results.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

Why isn't 35 × 25 the biggest since 35 is the largest number?

+

Great question! While 35 is the largest individual factor, multiplication depends on both numbers. When 35 is paired with 25, the product is actually smaller than 30 × 30 because the factors are more balanced in the second case.

Is there a pattern to predict which will be larger without calculating?

+

Yes! When the sum of factors is the same (like 30+30=60, 32+28=60), the pair closest to being equal gives the largest product. But when sums differ, you must calculate to be sure.

What's the fastest way to multiply these numbers?

+

For numbers ending in 0 or 5, use shortcuts: $30 \times 30 = 3 \times 3 \times 100 = 900$ and $35 \times 25 = 35 \times \frac{100}{4} = \frac{3500}{4} = 875$

How do I avoid calculation errors with larger numbers?

+

Break down the multiplication: For 32 × 28, use $(30+2) \times (30-2) = 30^2 - 2^2 = 900 - 4 = 896$ or use the standard algorithm step by step.

Why do some factor pairs give such similar results?

+

Notice that 30×30, 32×28, and 33×27 all have factors that sum to 60! When factor sums are close, products tend to be close too. The more balanced the factors, the larger the product.

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Maximum Value Comparison: Selecting the Highest-Result Exercise

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