Compare Numbers to 4/2: Sorting Fractions, Decimals, and Percentages

Converting Number Types with Mixed Forms

Organise the values below into two groups of values greater than 42 \frac{4}{2} and values less than 42 \frac{4}{2} :

1.3,12,150%,7412,0.5 1.3,\frac{1}{2},150\%,\frac{74}{12},0.5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Decide whether smaller or larger than the given number
00:03 Let's calculate the portion
00:06 Multiply by 100 and convert to percentages
00:12 Now let's compare each number to the given number, and decide if it's larger or smaller
00:18 We can see that this number is definitely smaller than 2
00:22 This number is also smaller than 2
00:27 These percentages are smaller than 200 percent
00:32 Convert the fraction to a mixed number
00:35 Break down the whole number into remainder
00:45 Convert from whole fraction to whole number, and combine with mixed number
00:51 We can see that this number is larger than the given number
00:56 We can see that this number is smaller than 2
01:01 Now let's divide into groups, the group larger than and the group smaller than the given number
01:20 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

Organise the values below into two groups of values greater than 42 \frac{4}{2} and values less than 42 \frac{4}{2} :

1.3,12,150%,7412,0.5 1.3,\frac{1}{2},150\%,\frac{74}{12},0.5

2

Step-by-step solution

To solve this problem, we need to compare each given value with 42 \frac{4}{2} .

  • Calculate 42=2 \frac{4}{2} = 2 .

Now, convert all given values to decimals:

  • The value 1.3 1.3 is already in decimal form: 1.3 1.3 .
  • Convert 12 \frac{1}{2} to decimals: 0.5 0.5 .
  • Convert 150% 150\% to decimals by dividing by 100: 150100=1.5 \frac{150}{100} = 1.5 .
  • Calculate 74126.1667 \frac{74}{12} \approx 6.1667 .
  • 0.5 0.5 is already in decimal form: 0.5 0.5 .

Now, compare each value with 2 2 :

  • Values less than 2 2 : 1.3,12,150%,0.5 1.3, \frac{1}{2}, 150\%, 0.5 (i.e., 1.3,0.5,1.5,0.5 1.3, 0.5, 1.5, 0.5 ).
  • Values greater than 2 2 : 7412 \frac{74}{12} (i.e., approximately 6.1667 6.1667 ).

Therefore, the solution to the problem is:

1.3,12,150%,0.5<42 1.3, \frac{1}{2}, 150\%, 0.5 < \frac{4}{2}

7412>42 \frac{74}{12} > \frac{4}{2}

3

Final Answer

1.3,12,150%,0.5<42 1.3,\frac{1}{2},150\%,0.5<\frac{4}{2}

7412>42 \frac{74}{12}>\frac{4}{2}

Key Points to Remember

Essential concepts to master this topic
  • Reference Value: Always simplify the comparison value first (42=2 \frac{4}{2} = 2 )
  • Conversion Method: Convert all values to decimals: 150% = 1.5, 74126.17 \frac{74}{12} ≈ 6.17
  • Verification: Check each comparison: 1.3 < 2 ✓, 0.5 < 2 ✓, 6.17 > 2 ✓

Common Mistakes

Avoid these frequent errors
  • Converting percentages incorrectly
    Don't convert 150% by just removing the % symbol = treating it as 150 instead of 1.5! This makes the percentage seem much larger than it actually is. Always divide by 100 to convert percentages to decimals.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

22.1-12.0

FAQ

Everything you need to know about this question

Why do I need to convert everything to the same form?

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Converting to the same form (like decimals) makes comparisons much easier! It's hard to compare 7412 \frac{74}{12} with 150% directly, but comparing 6.17 with 1.5 is straightforward.

Should I always convert to decimals?

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Not necessarily! You could convert everything to fractions or percentages instead. Choose whichever form feels most comfortable for you to work with.

How do I convert fractions to decimals quickly?

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Simply divide the numerator by the denominator. For example: 7412=74÷12=6.1667... \frac{74}{12} = 74 ÷ 12 = 6.1667...

What if the reference value was a decimal instead?

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The process is the same! If comparing to 2.5, you'd still convert all values to decimals and then compare each one to 2.5.

Do I need exact decimal values or can I use approximations?

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For comparisons, approximations are usually fine. 74126.17 \frac{74}{12} ≈ 6.17 is clearly greater than 2, so you don't need all decimal places!

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