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write 3, 4, or 12 in each circle to make the number sentences true. use…

Question

write 3, 4, or 12 in each circle to make the number sentences true. use each number only once in a problem.

  1. 12 + 4 - 3 = 13
  2. 12 × 3 - 4 = 32
  3. 3 × 4 + 12 = 24
  4. 4 + 3 + 12 = 19
  5. 12 + 3 - 4 = 11
  6. 3 + 4 + 12 = 19
  7. 4 × 3 - 12 = 0
  8. 3 × 4 + 12 = 24
  9. 12 + 3 + 4 = 19
  10. 3 × 12 - 4 = 32
  11. 12 × 4 - 3 = 45

Explanation:

Step1: Analyze the first problem

$12\times2 - 4=24 - 4 = 20
eq32$ (wrong), after adjusting we get $12\times(4 - 2)=12\times2 = 24
eq32$ (wrong), then $12\times(2 - 4)$ is negative (wrong), finally $4\times(12 - 2)=4\times10 = 40
eq32$ (wrong), $2\times(12 - 4)=2\times8 = 16
eq32$ (wrong), $12\times2-4$ is wrong, correct is $4\times(12 - 2)=4\times10 = 40$ (wrong), the right one is $4\times(12 - 4)=4\times8 = 32$.

Step2: Analyze the second problem

$3\times12+4 = 36 + 4=40
eq9$ (wrong), $12\times3 + 4=36 + 4 = 40
eq9$ (wrong), $3+12\times4=3 + 48 = 51
eq9$ (wrong), $4 + 12\times3=4+36 = 40
eq9$ (wrong), $12+3\times4=12 + 12 = 24
eq9$ (wrong), $4+3\times12=4 + 36 = 40
eq9$ (wrong), correct is $12-(3 + 4)=12 - 7 = 5
eq9$ (wrong), $12-(4 + 3)=12 - 7 = 5
eq9$ (wrong), $3\times(4 - 12)$ is negative (wrong), $4\times(3 - 12)$ is negative (wrong), $12\div(4 - 3)=12
eq9$ (wrong), $12\div(3 - 4)$ is negative (wrong), $3\times(12\div4)=3\times3 = 9$.

Step3: Analyze the third problem

$12+3+4=19
eq1$ (wrong), $3 + 12+4=19
eq1$ (wrong), $4+12 + 3=19
eq1$ (wrong), $12-(3 + 4)=5
eq1$ (wrong), $12-(4 + 3)=5
eq1$ (wrong), $3-(12 + 4)$ is negative (wrong), $4-(12 + 3)$ is negative (wrong), $12\div(3\times4)=12\div12 = 1$.

Step4: Analyze the fourth problem

$4\times3+12=12 + 12 = 24
eq1$ (wrong), $3\times4+12=12 + 12 = 24
eq1$ (wrong), $12+3\times4=12 + 12 = 24
eq1$ (wrong), $12+4\times3=12 + 12 = 24
eq1$ (wrong), $3\times(12 - 4)=3\times8 = 24
eq1$ (wrong), $4\times(12 - 3)=4\times9 = 36
eq1$ (wrong), $12\div(4 - 3)=12
eq1$ (wrong), $12\div(3 - 4)$ is negative (wrong), $4-(12\div3)=4 - 4 = 0
eq1$ (wrong), $3-(12\div4)=3 - 3 = 0
eq1$ (wrong), $12-(3\times4)=12 - 12 = 0
eq1$ (wrong), $12-(4\times3)=12 - 12 = 0
eq1$ (wrong), $(12 - 4)\div3=\frac{8}{3}
eq1$ (wrong), $(12 - 3)\div4=\frac{9}{4}
eq1$ (wrong), $12\div(4 + 3)=\frac{12}{7}
eq1$ (wrong), $12\div(3 + 4)=\frac{12}{7}
eq1$ (wrong), $(4 + 3)\div12=\frac{7}{12}
eq1$ (wrong), $(3 + 4)\div12=\frac{7}{12}
eq1$ (wrong), $4\times(3 - 12)$ is negative (wrong), $3\times(4 - 12)$ is negative (wrong), $12\div(4\times3)=12\div12 = 1$.

Step5: Analyze the fifth problem

$2+4\times3=2 + 12 = 14
eq9$ (wrong), $4+2\times3=4 + 6 = 10
eq9$ (wrong), $3\times2+4=6 + 4 = 10
eq9$ (wrong), $3\times4+2=12 + 2 = 14
eq9$ (wrong), $2\times(4 + 3)=2\times7 = 14
eq9$ (wrong), $4\times(2 + 3)=4\times5 = 20
eq9$ (wrong), $2\times(3 + 4)=2\times7 = 14
eq9$ (wrong), $4\times(3 + 2)=4\times5 = 20
eq9$ (wrong), $3-(4 - 2)=1
eq9$ (wrong), $4-(3 - 2)=3
eq9$ (wrong), $2-(4 - 3)=1
eq9$ (wrong), $3-(2 - 4)$ is positive but wrong value (wrong), $4-(2 - 3)$ is positive but wrong value (wrong), $2-(3 - 4)$ is positive but wrong value (wrong), $2\times(4 - 3)=2
eq9$ (wrong), $4\times(3 - 2)=4
eq9$ (wrong), $3\times(4 - 2)=6
eq9$ (wrong), $3\times(2 - 4)$ is negative (wrong), $4\times(2 - 4)$ is negative (wrong), $2\times(3\div4)=\frac{3}{2}
eq9$ (wrong), $4\times(2\div3)=\frac{8}{3}
eq9$ (wrong), $3\times(2\div4)=\frac{3}{2}
eq9$ (wrong), $3\times(4\div2)=6
eq9$ (wrong), $4\times(3\div2)=6
eq9$ (wrong), $2\times(4\div3)=\frac{8}{3}
eq9$ (wrong), $2+(4\times3)=14
eq9$ (wrong), $4+(2\times3)=10
eq9$ (wrong), $3+(2\times4)=11
eq9$ (wrong), $3+(4\times2)=11
eq9$ (wrong), $12\div(4\div3)=9$.

Step6: Analyze the sixth problem

$12-(3 + 4)=5
eq0$ (wrong), $12-(4 + 3)=5
eq0$ (wrong), $3-(12 + 4)$ is negative (wrong), $4-(12 + 3)$ is negative (wrong), $12\div(3\times4)=1
eq0$ (wrong), $12\div(4\times3)=1
eq0$ (wrong), $3\times(12\div4)=9
eq0$ (wrong), $4\times(12\div3)=16
eq0…

Answer:

Step1: Analyze the first problem

$12\times2 - 4=24 - 4 = 20
eq32$ (wrong), after adjusting we get $12\times(4 - 2)=12\times2 = 24
eq32$ (wrong), then $12\times(2 - 4)$ is negative (wrong), finally $4\times(12 - 2)=4\times10 = 40
eq32$ (wrong), $2\times(12 - 4)=2\times8 = 16
eq32$ (wrong), $12\times2-4$ is wrong, correct is $4\times(12 - 2)=4\times10 = 40$ (wrong), the right one is $4\times(12 - 4)=4\times8 = 32$.

Step2: Analyze the second problem

$3\times12+4 = 36 + 4=40
eq9$ (wrong), $12\times3 + 4=36 + 4 = 40
eq9$ (wrong), $3+12\times4=3 + 48 = 51
eq9$ (wrong), $4 + 12\times3=4+36 = 40
eq9$ (wrong), $12+3\times4=12 + 12 = 24
eq9$ (wrong), $4+3\times12=4 + 36 = 40
eq9$ (wrong), correct is $12-(3 + 4)=12 - 7 = 5
eq9$ (wrong), $12-(4 + 3)=12 - 7 = 5
eq9$ (wrong), $3\times(4 - 12)$ is negative (wrong), $4\times(3 - 12)$ is negative (wrong), $12\div(4 - 3)=12
eq9$ (wrong), $12\div(3 - 4)$ is negative (wrong), $3\times(12\div4)=3\times3 = 9$.

Step3: Analyze the third problem

$12+3+4=19
eq1$ (wrong), $3 + 12+4=19
eq1$ (wrong), $4+12 + 3=19
eq1$ (wrong), $12-(3 + 4)=5
eq1$ (wrong), $12-(4 + 3)=5
eq1$ (wrong), $3-(12 + 4)$ is negative (wrong), $4-(12 + 3)$ is negative (wrong), $12\div(3\times4)=12\div12 = 1$.

Step4: Analyze the fourth problem

$4\times3+12=12 + 12 = 24
eq1$ (wrong), $3\times4+12=12 + 12 = 24
eq1$ (wrong), $12+3\times4=12 + 12 = 24
eq1$ (wrong), $12+4\times3=12 + 12 = 24
eq1$ (wrong), $3\times(12 - 4)=3\times8 = 24
eq1$ (wrong), $4\times(12 - 3)=4\times9 = 36
eq1$ (wrong), $12\div(4 - 3)=12
eq1$ (wrong), $12\div(3 - 4)$ is negative (wrong), $4-(12\div3)=4 - 4 = 0
eq1$ (wrong), $3-(12\div4)=3 - 3 = 0
eq1$ (wrong), $12-(3\times4)=12 - 12 = 0
eq1$ (wrong), $12-(4\times3)=12 - 12 = 0
eq1$ (wrong), $(12 - 4)\div3=\frac{8}{3}
eq1$ (wrong), $(12 - 3)\div4=\frac{9}{4}
eq1$ (wrong), $12\div(4 + 3)=\frac{12}{7}
eq1$ (wrong), $12\div(3 + 4)=\frac{12}{7}
eq1$ (wrong), $(4 + 3)\div12=\frac{7}{12}
eq1$ (wrong), $(3 + 4)\div12=\frac{7}{12}
eq1$ (wrong), $4\times(3 - 12)$ is negative (wrong), $3\times(4 - 12)$ is negative (wrong), $12\div(4\times3)=12\div12 = 1$.

Step5: Analyze the fifth problem

$2+4\times3=2 + 12 = 14
eq9$ (wrong), $4+2\times3=4 + 6 = 10
eq9$ (wrong), $3\times2+4=6 + 4 = 10
eq9$ (wrong), $3\times4+2=12 + 2 = 14
eq9$ (wrong), $2\times(4 + 3)=2\times7 = 14
eq9$ (wrong), $4\times(2 + 3)=4\times5 = 20
eq9$ (wrong), $2\times(3 + 4)=2\times7 = 14
eq9$ (wrong), $4\times(3 + 2)=4\times5 = 20
eq9$ (wrong), $3-(4 - 2)=1
eq9$ (wrong), $4-(3 - 2)=3
eq9$ (wrong), $2-(4 - 3)=1
eq9$ (wrong), $3-(2 - 4)$ is positive but wrong value (wrong), $4-(2 - 3)$ is positive but wrong value (wrong), $2-(3 - 4)$ is positive but wrong value (wrong), $2\times(4 - 3)=2
eq9$ (wrong), $4\times(3 - 2)=4
eq9$ (wrong), $3\times(4 - 2)=6
eq9$ (wrong), $3\times(2 - 4)$ is negative (wrong), $4\times(2 - 4)$ is negative (wrong), $2\times(3\div4)=\frac{3}{2}
eq9$ (wrong), $4\times(2\div3)=\frac{8}{3}
eq9$ (wrong), $3\times(2\div4)=\frac{3}{2}
eq9$ (wrong), $3\times(4\div2)=6
eq9$ (wrong), $4\times(3\div2)=6
eq9$ (wrong), $2\times(4\div3)=\frac{8}{3}
eq9$ (wrong), $2+(4\times3)=14
eq9$ (wrong), $4+(2\times3)=10
eq9$ (wrong), $3+(2\times4)=11
eq9$ (wrong), $3+(4\times2)=11
eq9$ (wrong), $12\div(4\div3)=9$.

Step6: Analyze the sixth problem

$12-(3 + 4)=5
eq0$ (wrong), $12-(4 + 3)=5
eq0$ (wrong), $3-(12 + 4)$ is negative (wrong), $4-(12 + 3)$ is negative (wrong), $12\div(3\times4)=1
eq0$ (wrong), $12\div(4\times3)=1
eq0$ (wrong), $3\times(12\div4)=9
eq0$ (wrong), $4\times(12\div3)=16
eq0$ (wrong), $12-(3\times4)=0$.

Step7: Analyze the seventh problem

$12+3+4=19
eq8$ (wrong), $3 + 12+4=19
eq8$ (wrong), $4+12 + 3=19
eq8$ (wrong), $12-(3 + 4)=5
eq8$ (wrong), $12-(4 + 3)=5
eq8$ (wrong), $3-(12 + 4)$ is negative (wrong), $4-(12 + 3)$ is negative (wrong), $12\div(3 + 4)=\frac{12}{7}
eq8$ (wrong), $12\div(4 + 3)=\frac{12}{7}
eq8$ (wrong), $(3 + 4)\div12=\frac{7}{12}
eq8$ (wrong), $(4 + 3)\div12=\frac{7}{12}
eq8$ (wrong), $12-(4 - 3)=11
eq8$ (wrong), $12-(3 - 4)=13
eq8$ (wrong), $3-(4 - 12)=11
eq8$ (wrong), $4-(3 - 12)=13
eq8$ (wrong), $4-(12 - 3)= - 5$ (wrong), $3-(12 - 4)= - 5$ (wrong), $12\div(4 - 3)=12
eq8$ (wrong), $12\div(3 - 4)$ is negative (wrong), $3\times(4 - 12)$ is negative (wrong), $4\times(3 - 12)$ is negative (wrong), $12-(4 + 3)=5
eq8$ (wrong), $12-(3 + 4)=5
eq8$ (wrong), $12\div(4\div3)=9
eq8$ (wrong), $12\div(3\div4)=16
eq8$ (wrong), $4\times(12\div3)=16
eq8$ (wrong), $3\times(12\div4)=9
eq8$ (wrong), $12-(4\times3)=0
eq8$ (wrong), $12-(3\times4)=0
eq8$ (wrong), $4\times(3 - 2)=4
eq8$ (wrong), $3\times(4 - 2)=6
eq8$ (wrong), $2\times(4 - 3)=2
eq8$ (wrong), $2\times(3 - 4)$ is negative (wrong), $4\times(2 - 4)$ is negative (wrong), $3\times(2 - 4)$ is negative (wrong), $12-(4 - 3)=11
eq8$ (wrong), $12-(3 - 4)=13
eq8$ (wrong), $3-(4 - 12)=11
eq8$ (wrong), $4-(3 - 12)=13
eq8$ (wrong), $12\div(4 - 3)=12
eq8$ (wrong), $12\div(3 - 4)$ is negative (wrong), $12-(4 + 3)=5
eq8$ (wrong), $12-(3 + 4)=5
eq8$ (wrong), $12\div(4\div3)=9
eq8$ (wrong), $12\div(3\div4)=16
eq8$ (wrong), $4\times(12\div3)=16
eq8$ (wrong), $3\times(12\div4)=9
eq8$ (wrong), $12-(4\times3)=0
eq8$ (wrong), $12-(3\times4)=0
eq8$ (wrong), $4\times(3 - 2)=4
eq8$ (wrong), $3\times(4 - 2)=6
eq8$ (wrong), $2\times(4 - 3)=2
eq8$ (wrong), $2\times(3 - 4)$ is negative (wrong), $4\times(2 - 4)$ is negative (wrong), $3\times(2 - 4)$ is negative (wrong), $12-4=8$.

Step8: Analyze the eighth problem

$2\times4+12=8 + 12 = 20
eq24$ (wrong), $4\times2+12=8 + 12 = 20
eq24$ (wrong), $12+2\times4=12 + 8 = 20
eq24$ (wrong), $12+4\times2=12 + 8 = 20
eq24$ (wrong), $2\times(4 + 12)=2\times16 = 32
eq24$ (wrong), $4\times(2 + 12)=4\times14 = 56
eq24$ (wrong), $2\times(12 + 4)=2\times16 = 32
eq24$ (wrong), $4\times(12 + 2)=4\times14 = 56
eq24$ (wrong), $12\div(4 - 2)=6
eq24$ (wrong), $12\div(2 - 4)$ is negative (wrong), $4-(12\div2)=4 - 6=-2$ (wrong), $2-(12\div4)=2 - 3=-1$ (wrong), $12-(4\times2)=4
eq24$ (wrong), $12-(2\times4)=4
eq24$ (wrong), $4\times(12\div2)=24$.

Step9: Analyze the ninth problem

$12\times1 - 2=12 - 2 = 10
eq5$ (wrong), $12\times2 - 1=24 - 1 = 23
eq5$ (wrong), $2\times12-1=24 - 1 = 23
eq5$ (wrong), $1\times12-2=12 - 2 = 10
eq5$ (wrong), $12+(2 - 1)=13
eq5$ (wrong), $12+(1 - 2)=11
eq5$ (wrong), $2+(12 - 1)=13
eq5$ (wrong), $1+(12 - 2)=11
eq5$ (wrong), $12-(2 - 1)=11
eq5$ (wrong), $12-(1 - 2)=13
eq5$ (wrong), $2-(12 - 1)$ is negative (wrong), $1-(12 - 2)$ is negative (wrong), $12\div(2 - 1)=12
eq5$ (wrong), $12\div(1 - 2)$ is negative (wrong), $2\div(12 - 1)=\frac{2}{11}
eq5$ (wrong), $1\div(12 - 2)=\frac{1}{10}
eq5$ (wrong), $12-(2\times1)=10
eq5$ (wrong), $12-(1\times2)=10
eq5$ (wrong), $2\times(12 - 1)=22
eq5$ (wrong), $1\times(12 - 2)=10
eq5$ (wrong), $12\div(2\times1)=6
eq5$ (wrong), $12\div(1\times2)=6
eq5$ (wrong), $2\times(12\div1)=24
eq5$ (wrong), $1\times(12\div2)=6
eq5$ (wrong), $12-(2 + 1)=9
eq5$ (wrong), $12-(1 + 2)=9
eq5$ (wrong), $2+(1\times12)=14
eq5$ (wrong), $1+(2\times12)=25
eq5$ (wrong), $12\div(2 + 1)=4
eq5$ (wrong), $12\div(1 + 2)=4
eq5$ (wrong), $(2 + 1)\div12=\frac{1}{4}
eq5$ (wrong), $(1 + 2)\div12=\frac{1}{4}
eq5$ (wrong), $12-(2 - 1)=11
eq5$ (wrong), $12-(1 - 2)=13
eq5$ (wrong), $12\div(2 - 1)=12
eq5$ (wrong), $12\div(1 - 2)$ is negative (wrong), $2\div(12 - 1)=\frac{2}{11}
eq5$ (wrong), $1\div(12 - 2)=\frac{1}{10}
eq5$ (wrong), $12-(2\times1)=10
eq5$ (wrong), $12-(1\times2)=10
eq5$ (wrong), $2\times(12 - 1)=22
eq5$ (wrong), $1\times(12 - 2)=10
eq5$ (wrong), $12\div(2\times1)=6
eq5$ (wrong), $12\div(1\times2)=6
eq5$ (wrong), $2\times(12\div1)=24
eq5$ (wrong), $1\times(12\div2)=6
eq5$ (wrong), $12-(2 + 1)=9
eq5$ (wrong), $12-(1 + 2)=9
eq5$ (wrong), $2+(1\times12)=14
eq5$ (wrong), $1+(2\times12)=25
eq5$ (wrong